JC-NRLF 


43D 


I.IHKAK'Y 

or  TIIF. 

UNIVERSITY  OF  CALIFORNIA 


Gil""]    OK 


S  . 


Class 


w.  is.  XV  :ur,. 


U.  S.  DEPARTMENT  OF  AGRICULTURE. 

WEATHKH     r,F  1!  F.AIT. 


STUDIES  ON  THE  CIRCULATION  OE  THE  ATMOSPHERES  OE 

THE  SUN  AND  OF  THE  EARTH. 


from  the  Monthly  Weather  Review,  October  and  November,  1903,  and  January,  February,  April,  May,  and  June,  11)04. 


FRANK    H.    BIGELOW.    M.  A.,    L.  H.  D. 


i.  I  -.-in;    M|      MM  |'U 


Prepared  under  the  direction  of  WILLIS    L.    MOORE,  Chief  U.  S.   Weather  Bureau. 


1 


WASHINGTON: 

w  BA-TH1  \  I    . 

1904. 


W.  B.  No.  316. 


U.  S.  DEPARTMENT  OF  AGRICULTURE, 

WEATHER    BUREAU. 


STUDIES  ON  THE  CIRCULATION  OF  THE  ATMOSPHERES  OF 

THE  SUN  AND  OF  THE  EARTH. 


Reprints  from  the  Monthly  Weather  Review,  October  and  November,  1903,  and  January,  February,  April,  May,  and  June,  1904. 


BY 


FRANK    H.    BIGELOW,    M.  A.,    L.  H.  D., 


PROFESSOH   OF  METEOROLOGY. 


Prepared  under  the  direction  of  WILLIS   L.   MOORE,  Chief  U.  S.  Weather  Bureau. 


WASHINGTON: 

WEATHER      BUREAU. 
1904. 


OOISTTElsTTS. 


Page. 

I. — The  circulation  of  the  sun's  atmosphere 

Historical  review 1 

Compilation  of  the  prominence  observations 2 

Discussion  of  the  observations  4 

The  differential  circulation  within  the  sun 6 

II. — Synchronism  of  the  variations  of  the  solar  prominences  with 

the  terrestrial  barometric  pressures  and  the  temperatures. .  9 

Several  opinions  on  the  subject  of  synchronism 9 

The  unsatisfactory  state  of  the  observational  data 11 

Kesults  of  the  observations  ., 14 

Discussion  of  the  local  inversions 15 

III. — The  problem  of  the  general  circulation  of  the  atmosphere  of 

the  earth 17 

The  canal  theory  17 

The  general  equations  of  motion 

Line  integrals  in  the  atmosphere 17 

Equivalent  expressions  for  the  density  p 18 

P  dr 

Development  of  the  terms  —  ,  V,  and  ^ 

To  find  the  direction  of  the  boundary  curve  between  two  strata .  19 
Case  I. — Applicable  to  the  temperate  and  polar  latitudes 

of  the  earth 19 

Case  II. — Applicable  to  the  tropical  zones  of  the  earth ....  19 
Case  III. — Applicable  to  the  atmospheres  of  the  sun,  Jupi- 
ter, and  Saturn 20 

The  interaction  of  Case  I  and  Case  II  in  the  earth's  atmosphere 

in  the  formation  of  local  cyclones  and  anticyclones 20 

IV. — Values  of  certain  meteorological  quantities  for  the  sun 23 

The  importance  of  these  values  to  terrestrial  meteorology ....  23 

Nipher's  equations 23 

The  astronomical  constants  for  the  earth  and  the  sun 24 

Application  of  the  thermodynamic  formula  to  the  gaseous  en- 
velope of  the  sun 25 

Distribution  of  the  pressure,  temperature,  and  density  in  a 

solar  hydrogen  atmosphere 27 

Discussion  of  the  values  derived  from  tables  12  to  14 29 

The  density 29 

The  pressure 29 

The  temperature  and  the  gas  constant 29 

The  mass  of  sun,  the  weight  of  one  gram  on  the  surface  of 

the  sun,  and  the  transformation  factor 30 

Specific  heats,  energy  of  radiation,  and  contraction 30 

V. — Results  of  the  nephoscope  observations  in  the  West  Indies 

during  the  years  1899-1903 : 31 

Methods  of  observation  and  reduction 31 

Charts  of  the  resulting  velocities  and  directions  of  motion  for 

the  West  Indies 31 

The  arch  spanning  the  Tropics,  which  divides  the  eastward 

drift  from  the  westward  drift  in  the  general  circulation ....  32 

The  levels  of  maximum  horizontal  velocity 32 

The  winter  and  the  summer  circulations 33 

The  cause  of  the  West  Indian  hurricanes 33 

Approximate  normal  circulation  in  the  West  Indies  during  the 

winter  and  summer,  respectively 34 

VI. — The  circulation  in  cyclones  and  anticyclones,  with  precepts 
for  forecasting  by  auxiliary  charts  on  the  3500-foot  and  the 

10,000-foot  planes 35 

The  structure  of  the  isobars  at  different  levels 35 

The  geometrical  construction  of  high  and  low  pressure  areas .  35 

The  cusp  formation  and  its  changes 37 

Critical  remarks  regarding  several  theories  of  cyclones  and 

anticyclones 38 

The  cause  of  the  counter  currents  in  the  lower  strata 38 

Precepts  for  forecasting  with  the  charts  on  the  3500-foot  and 

the  10,000-foot  planes  as  auxiliaries 39 

1.  Direction  of  the  storm  tracks 39 

2.  The  velocity  of  advance 39 

3.  The  areas  of  precipitation 39 

4.  Penetration  into  the  higher  levels 39 

VII. — The  average  monthly  vectors  of  the  general  circulation  in 

the  United  States 41 

8549 


TABLES. 


Page. 


Table  1.  —  The  prominence  energy  in  zones  as  collected  on  the  26.68- 

day  period,  showing  retardation  in  different  latitudes  .          3 

2.  —  Eetardation  of  the  sun  in  different  latitudes  as  derived 

from  the  prominence  frequency  in  longitude  .........          4 

3.  —  Mean  retardation  by  zones  ............................  5 

4.  —  Bigelow's  rotation  periods  ............................          5 

5.  —  Transformations    of    the    daily  angular    velocity    into 

sidereal  and  synodic  periods  ........................          6 

6.  —  Several  determinations  of  the  rotation  periods  of  the 

solar  spots  in  different  latitudes  ....................          6 

7.  —  Astronomical  constants  ...............................         25 

8.  —  Constants  for  one  atmosphere  of  hydrogen  on  the  earth  .         25 

9.  —  Transition  to  constants  for  a  solar  hydrogen  atmosphere  .         25 

10.  —  Fundamental  constants  for  a  hydrogen  atmosphere  on 

the  sun  ............................................         26 

11.  —  Distribution  of  the  pressure,  temperature,  and  density 

in  the  solar  hydrogen  atmosphere  ...................        27 

12.  —  Computation  of  the  pressures,  temperatures  and  den- 

sities at  the  surface  and  within  the  sun,  by  Nipher's 
formulas  ......  '  ....................................        28 

13.  —  Transformation  factor  from  perfect  gases  to  the  material 

of  the  sun  within  the  photosphere  ...................         28 

14.  —  Specific  heats  cp,  cv,  quantity  of  heat  Q,  and  work  W,  in 

the  surface  stratum  of  the  sun  ......................        28 

15.  —  Form  for  computing  the  coordinates  of  the  resultant 

curve  .............................................        36 

16.  —  Average  monthly  vectors  of  the  general  circulation  in 

the  United  States,  1896-97  .........................         42 


Figure  1.- 
2.- 
3.- 
4.- 

5.- 
6.- 

7.- 
8.- 
9.- 

10. 
11. 

12. 

13. 

14. 

15. 

16. 

17.- 

18.- 

19.- 

20.- 

21.- 
22.- 
23.- 
24.- 
25.- 
26.- 


ILLUSTRATIONS. 

-Retardation  of  rotation  in  different  zones  of  the  sun  as 

derived  from  the  prominence  frequency  in  longitude  . 
-Periods  of  rotation  of  the  solar  photosphere  derived 

from  the  prominence  frequency  in  different  zones  ---- 
-Variable  retardations  in  the  periods  of  rotation  of  the 

solar  photosphere  ................................. 

-Formation  of  vortices  in  the  solar  mass  by  differential 

rotations  ......................................... 

-Solar  and  terrestrial  synchronism  .................... 

-Variations  of  the  annual  pressure  in  the  direct  type  .  .  . 
-Variations  of  the  annual  pressure  in  the  inverse  type  . 
-Variations  of  the  annual  pressure  in  the  indifferent  type  . 
-Variations  of  the  annual  temperature  in  the  direct 


type. 


Variations  of  the  annual  temperature  in  the  inverse 
type 

Variations  of  the  annual  temperature  in  the  indiffer- 
ent type 

Distribution  of  the  pressure  types 

Distribution  of  the  temperature  types 

Component  axes 

— Case  I 

-Case  II 

-Case  III 

-Cases  I  and  II  unmodified 

-Cases  I  and  II  as  modified 

-Pressures  at  different  latitudes  (Ferrel)  and  altitudes 
(Sprung) 

-Distribution  of  the  pressure,  temperature,  and  density, 
in  a  solar  hydrogen  atmosphere  

-Chart  XII  A.  Average  monthly  vectors  of  the  general 
circulation,  Havana,  Cuba. 

-Chart  XII  A.  Average  monthly  vectors  of  the  general 
circulation,  Cienfuegos,  Cuba. 

-Chart  XII  A.  Average  monthly  vectors  of  the  general 
circulation,  Santiago,  Cuba. 

-Chart  XII  A.  Average  monthly  vectors  of  the  general 
circulation,  Kingston,  Jamaica. 

-Chart  XII  B.  Average  monthly  vectors  of  the  general 
circulation,  Santo  Domingo,  Santo  Domingo. 

iii 


8 
10 
10 
11 
11 

12 
13 

13 
14 
14 
18 
19 
20 
20 
21 
21 

21 
27 


IV 


27. — Chart  XII  B.     Average  monthly  vectors  of  the  general 

circulation,  San  Juan,  Porto  Kico. 
28.— Chart  XII  B.     Average  monthly  vectors  of  the  general 

circulation,  Basseterre,  St.  Kitts. 
29. — Chart  XII  B.     Average  monthly  vectors  of  the  general 

circulation,  Roseau,  Dominica. 
30. — Chart  XII  C.     Average  monthly  vectors  of  the  general 

circulation,  Bridgetown,  Barbados. 
31. — Chart  XII  C.     Average  monthly  vectors  of  the  general 

circulation,  Willemstad,  Cura9ao. 
32. — Chart  XII  C.     Average  monthly  vectors  of  the  general 

circulation,  Port  of  Spain,  Trinidad. 
33. — Chart  XIII  A.     Average  monthly  vectors  of  the  general 

circulation,  Havana,  Cuba. 
34. — Chart  XIII  A.     Average  monthly  vectors  of  the  general 

circulation,  Cienfuegos,  Cuba. 
35. — Chart  XIII  A.     Average  monthly  vectors  of  the  general 

circulation,  Santiago,  Cuba. 
36. — Chart  XIII  A.     Average  monthly  vectors  of  the  general 

circulation,  Kingston,  Jamaica. 
37. — Chart  XIII  B.     Average  monthly  vectors  of  the  general 

circulation,  Santo  Domingo,  Santo  Domingo. 
38. — Chart  XIII  B.     Average  monthly  vectors  of  the  general 

circulation,  San  Juan,  Porto  Kico. 
39.— Chart  XIII  B.     Average  monthly  vectors  of  the  general 

circulation,  Basseterre,  St.  Kitts. 
40. — Chart  XIII  B.     Average  monthly  vectors  of  the  general 

circulation,  Roseau,  Dominica. 
41. — Chart  XIII  C.     Average  monthly  vectors  of  the  general 

circulation,  Bridgetown,  Barbados. 
42. — Chart  XIII  C.     Average  monthly  vectors  of  the  general 

circulation,  Willemstad,  Cura9ao. 
43. — Chart  XIII  C.     Average  monthly  vectors  of  the  general 

circulation,  Port  of  Spain,  Trinidad. 
44. — Chart  XIV  A.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  surface. 
45. — Chart  XIV  A.     Average  summer  vectors  of  the  general 

circulation-  in  the  West  Indies,  stratus  level. 
46. — Chart  XIV  A.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  cumulus  level. 
47. — Chart  XIV  A.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  strato-cumulus  level. 
48. — Chart  XIV  A.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  alto-cumulus  level. 
49. — Chart  XIV  A.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  alto-stratus  level. 
50. — Chart  XIV  B.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  cirro-cumulus  level. 
51. — Chart  XIV  B.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  cirro-stratus  level. 
52. — Chart  XIV  B.     Average  summer  vectors  of  the  general 

circulation  in  the  West  Indies,  cirrus  level. 
53.— Chart  XIV  B.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  surface. 
54. — Chart  XIV  B.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  stratus  level. 
55. — Chart  XIV  B.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  cumulus  level. 


Page. 


56. — Chart  XIV  C.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  strato-cumulus  level. 
57. — Chart  XIV  C.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  alto-Cumulus  level. 
58. — Chart  XIV  C.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  alto-stratus  level. 
59. — Chart  XIV  C.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  cirro-cumulus  level. 
60.  — Chart  XIV  C.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  cirro-stratus  level. 
61. — Chart  XIV  C.     Average  winter  vectors  of  the  general 

circulation  in  the  West  Indies,  cirrus  level. 
62. — Mean  altitudes  at  which  the  westward  drift  reverses 

to  the  eastward  drift  in  the  Tropics 

63. — Chart  XII.     Sea  level  isobars  for  February  3,  1903. 
64.— Chart  XII.     Isobars  on  the  3500-foot  and  the  10,000- 
foot  levels  for  February  3,  1903. 
65. — Chart  XIII.     Normal   and   abnormal  isobars  on   the 

3500-foot  plane  for  February  3,  1903. 
66.— Chart  XIII.     Normal   and   abnormal   isobars  on  the 

10,000-foot  plane  for  February  3,  1903. 
67.— Chart  XIV.     Typical  normal  sea-level  isobars. 
68. — Chart  XIV.     Typical  normal  3500-foot  plane  isobars. 
69.— Chart  XIV.     Typical  normal  10,000-foot  plane  isobars. 
70. — Chart  XIV.     Typical  abnormal  sea-level  isobars. 
71.— Chart  XIV.     Typical  abnormal  3500-foot  plane  isobars. 
72.— Chart  XIV.    Typical  abnormal  10,000-foot  plane  isobars. 
73.— Chart  XV.     Isobars  and  isotherms  for  February  27, 


Pago. 


Temperature  components  for  February  27, 


Chart  XIV. 
Chart  XIV. 
Chart  XIV. 
Chart  XIV. 
Chart  XIV. 
Chart  XV. 

1903. 
74.— Chart  XV. 

1903. 

75. — The  general  ellipse 

76. — Bight  lines  and  circles  where  the  gradients  are  twice 

as  great  on  the  circles  as  on  the  right  lines 

77. — Chart  XI.     Average  monthly  vectors  of  the  general 

circulation,  St.  Paul,  Minn. 
78. — Chart  XI.     Average  monthly  vectors  of  the  general 

circulation,  Kansas  City,  Mo. 
79. — Chart  XI.     Average  monthly  vectors  of  the  general 

circulation,  Abilene,  Tex. 
80. — Chart  XI.     Average  monthly  vectors  of  the   general 

circulation,  Vicksburg,  Miss. 
81. — Chart  XII.     Average  monthly  vectors  of  the  general 

circulation,  Louisville,  Ky. 
82. — Chart  XII.     Average  monthly  vectors  of  the  general 

circulation,  Detroit,  Mich. 
83. — Chart  XII.     Average  monthly  vectors  of  the  general 

circulation,  Cleveland,  Ohio. 
84.— Chart  XII.     Average  monthly  vectors  of  the  general 

circulation,  Buffalo,  N.  Y. 
85.— Chart  XIII.     Average  monthly  vectors  of  the  general 

circulation,  Blue  Hill,  Mass. 
86. — Chart  XIII.     Average  monthly  vectors  of  the  general 

circulation,  Washington,  D.  C. 
87. — Chart  XIII.     Average  monthly  vectors  of  the  general 

circulation,  Waynesville,  N.  C.,  and  Ocean  City,  Md. 
88.— Chart  XIII.     Average  monthly  vectors  of  the  general 

circulation,  Key  West,  Fla. 


32 


36 
36 


STUDIES  ON  THE  CIRCULATION  OF  THE  ATMOSPHERES  OF  THE  SUN  AND  OF 

THE  EARTH. 


I.— THE  CIRCULATION  OF  THE  SUN'S  ATMOSPHERE. 


HISTORICAL    REVIEW. 

That  the  solar  atmosphere  is  circulating  in  accordance  with 
the  laws  governing  the  convective  and  radiative  action  of  a 
large  mass  of  matter  contracting  by  its  own  gravitation,  is  so 
evident  that  numerous  efforts  have  been  made  to  determine 
what  these  laws  are,  or  at  least  to  discover  some  reliable  clue 
to  a  beginning  of  scientific  research  in  that  direction.  The 
application  by  K.  Emden'  of  H.  von  Helmholtz's  method  of 
adapting  the  general  equations  of  motion  to  a  solar  mass,  ap- 
peared to  be  a  step  in  the  right  direction;  further  attention 
was  called  to  the  possibilities  of  this  solution  in  my  Report  on 
Eclipse  Meteorology,2  pages  71-74.  In  June,  1902,  Sir  Nor- 
man Lockyer  and  Dr.  W.  J.  S.  Lockyer 3  published  their  sug- 
gestive curve  of  the  percentage  frequency  of  the  solar  prom- 
inences derived  from  the  Italian  observations  for  each  10°  of 
solar  latitude  north  and  south  of  the  equator.  This  curve  in- 
terested me  because  it  appeared  to  identify  the  distinctly  solar 
phenomena  with  the  short  period  curves  which  I  had  worked  out 
in  the  terrestrial  magnetic  field  and  in  the  meteorological  field 
of  the  United  States,  and  first  published  in  December,  1894,4  af- 
terwards republishing  them  in  1898.5  A  study  of  the  difficult  sub- 
ject of  inversion  of  periodic  effects  in  magnetic  and  meteorolo- 
gical phenomena  discovered  at  that  time  has  been  actively  pur- 
sued by  the  Weather  Bureau  for  the  past  ten  years,  and  evidence 
is  being  accumulated,  not  only  here  but  by  others,  of  the  exist- 
ence and  importance  of  the  fact  of  inversion  in  the  magnetic 
phenomena,  the  pressures,  and  the  temperatures  of  the  earth 
generally.  The  solar  prominence  curve  suggested  also  the  pos- 
sibility of  obtaining  more  decisive  evidence  of  solar  and  terres- 
trial synchronisms  than  that  afforded  by  the  solar-spot  fre- 
quency curve  (which  is  apparently  only  a  sluggish  register  of 
the  true  solar  output  of  energy),  because  the  terrestrial  mag- 
netic field  and  the  meteorological  elements  show  minor  varia- 
tions that  are  only  feebly  indicated  in  the  solar-spot  curve. 
The  prominence  frequency  curves  brought  out  distinctly  for 
the  sun  the  minor  fluctuations  that  had  been  already  found  in 
the  earth's  atmosphere. 

My  first  computations  on  the  amplitudes  of  the  deflecting 
forces  which  disturb  the  normal  terrestrial  magnetic  field  were 
computed  for  the  years  1878-1893,  using  the  records  of  several 
European  magnetic  stations.  To  have  extended  the  same  com- 
putation to  the  years  1841-1900,  inclusive,  would  have  re- 
quired a  vast  amount  of  labor;  as  an  equivalent,  the  de- 
flections of  the  horizontal  force  alone,  without  the  declination 

1  Eine  Beobachtung  uber  Luftwogen.    R.  Emden.   Wied.  Ann.  LXII 
p.  62,  1897,  and  Astrophysical  Journal,  January,  1902. 

2  Eclipse  Meteorology  and  Allied  Problems.  Frank  H.  Bigelow    Weather 
Bureau  Bulletin  I.     1902. 

3  On  some  Phenomena  which  suggest  a  short  Period  of  Solar  and  Me- 
teorological Changes.     By  Sir  Norman  Lockyer,  K.  C.  B.,  F.  E   S    and 
William  J.  S.  Lockyer,  M.  A.,  Ph.   D.,  F.  R.  A.  S.     Received  June  14 
Read  June  19, 1902.  Addendum.  Dated  June  26.    Proc.  Roy.  Soc.    Vol.70 

4  Inversion  of  Temperatures  in  the  26.68  Day  Solar  Magnetic  Period 
Frank  H.  Bigelow.    Am.  Jour.  Sci.     Vol.  XLVIII,  December,  1894. 

5  Report  on  Solar  and  Terrestrial  Magnetism  in  their  Relations  to  Me- 
teorology.    Frank  H.  Bigelow.     Weather  Bureau  Bulletin  No.  21.     1898 


and  vertical  components,  were  derived  by  the  construction  of 
a  series  of  graphical  curves  covering  these  sixty  years,  from 
which  the  mean  ordinates  were    computed.     The  result  was 
shown  in  my  paper  on  Cosmical  Meteorology,  July,  1902.6     The 
same  variation  curve  was  found  from  the  horizontal  force  for 
the  years   1878-1893  as  that  previously  given  by   the   com- 
puted a  curve,  and  it  was  therefore  proper  to  conclude  that 
this  extension  of  the  original  computation  in  both  directions 
was  sufficiently  correct   for   the   purpose   of   the  discussion. 
Furthermore,  the  prominence  frequencies  presented  the  ma- 
terial for  studying  the  solar  activity  by  zones,  and  the  result 
of  my  compilation  to  determine  the  law  of  the  movement  of 
the  points  of  prominence  maxima  in  latitude  was  read  before 
the  American  Association  for  the  Advancement  of  Science  on 
December  28,  1902,  and  published  in  the  MONTHLY  WEATHER 
REVIEW,  January,  1903.7     I  there  showed  that  in  each  hemis- 
phere the  maxima  of  prominence  frequency  are  grouped  in  two 
zones,  and  that  in  the  zones  near  the  equator,  in  latitudes  about 
20°,  the  maxima  of  frequency  approach  that  plane  in  common 
with  the  sun  spots  and  faculse  during  the  11-year  period,  while 
in  the  zones  in  latitudes  50°-70°,  the  maxima  simultaneously 
move  toward  the  poles.     This  indicates  a  characteristic  ten- 
dency of   the  solar  circulation  to  spread  from  the  middle  lati- 
tudes toward  the  equator  and  toward  the  poles  in  two  inde- 
pendent branches.     In  a  paper8  published  in  March,  1903,  the 
Lockyers  obtained  a  similar  result  for  the  same  phenomena. 
They  gave  the  life  history  of  the  sun  in  the  separate  11-year 
periods  between  1872-1901,  whereas  my  paper  had  grouped 
these  three  available  periods  together  for  the  sake  of  finding 
the  average  law.     Dr.  A.  Ricco9  has  published  similar  studies 
of  the  movements  of   prominences  in  latitude  for  the  years 
1880-1902.     The  subject  of   the  average  distribution  of   the 
solar  spots  in  longitude  on  the  sun  has  been  discussed  by  Dr. 
A.  Wolfer,10  and  from  it  he  derived  some  determinations  of  the 
solar  rotation  in  different  latitudes.     In  my  paper  of  January, 
1903,  I  stated  that  besides  a  study  of  the  variable  distribu- 
tion of  the  prominences  in  latitude,  an  effort  was  being  made 
by  me  to  discover  some  clue  as  to  their  distribution  in  longi- 
tude, in  order  to  learn  whether  or  not  there  was  an  accumula- 
tion   on  certain  meridians,  and  it  is  the  result  of  this  work 
that  is  contained  in  the  present  paper.     We  have  discovered 
an  unexpectedly  clear  insight  into  the  solar  circulation,  and 
this  tends  to  strengthen  the  line  of  argument  which  I  have 
been  developing  during  the  past  fifteen  years  to  explain  the 

6  A  Contribution  to  Cosmical  Meteorology.  Monthly  Weather  Review 
July,  1902,  Vol.  XXX,  p.  347. 

'Synchronous  Changes  in  the  Solar  and  Terrestrial  Atmosphere. 
Monthly  Weather  Review,  January,  1903,  Vol.  XXXI,  p.  9. 

8Solar  Prominence  and  Spot  Circulation,  1872-1901,  By  Sir  Norman 
Lockyer,  K.  C.  B.,  F.  R.  S.,  and  William  J.  S.  Lockyer,  Chief  Assistant, 
Solar  Physics  Observatory,  M.  A.  fCamb.),  Ph.  D.  (Gott)  F  R  A  S 
Received  March  17.  Read  March  26,  1903.  Proc.  Roy.  Soc.  Vol.  71. 

9Le  protuberanze  solari  nello'ultimo  periodo  undecennale.  Mem 
Spett.  Ital.,  Vol.  XXXII,  1903.  A.  Ricco. 

10Publikationen  dor  Sternwarte  des  Eidg.  Poly  tech.  Inst.,  Zurich  A 
Wolfer.  Bd.  I,  II,  III,  1897,  1899,  1902. 


mysterious    synchronism    at    the   earth,  of   which  numerous 
symptoms  have  been  noted,  in  many  kinds  of  observations. 

COMPILATION  OF  THE  PROMINENCE  OBSERVATIONS. 

The  prominences  which  appear  on  the  edge  of  the  disk  of 
the  sun  have  been  carefully  delineated  by  the  Italian  observ- 
ers Secchi  and  Tacchini  with  stations  at  Rome  and  Palermo, 
also  Kicco  and  Mascari,  at  Catania,  working  in  cooperation, 
from  March,  1871,  till  the  present  time  in  an  unbroken  series. 
Students  of  solar  physics  can  not  too  gratefully  acknowledge 
the  value  of  the  patient,  laborious  work  which  has  been  done 
by  these  observers,  and  the  practical  study  of  these  data  is 
likely  to  open  up  new  and  important  lines  of  research.  Be- 
ginning with  March  1,  1871,  the  images  of  the  solar  disk  have 
been  published  in  the  Memorie  della  Societa  degli  Spettro- 
scopisti  Italiani,  and  they  cover  the  time  to  the  end  of  the 
century,  except  for  a  long  gap  from  September,  1877,  to  Jan- 
uary, 1884.  I  am  informed  by  Dr.  Eicco  that  the  drawings 
for  these  missing  years  are  in  the  archives  of  the  Catania  Ob- 
servatory, and  it  is  obvious  that  steps  should  be  taken  as  soon 
as  practicable  to  complete  the  published  record,  because  the 
demand  for  the  data  is  sure  to  increase,  as  can  be  inferred 
from  the  results  indicated  in  this  paper.  On  those  graphical 
tables  certain  lines  were  drawn  showing  the  position  of  the 
north  and  south  poles  and  the  equator  of  the  sun,  so  that 
the  disk  could  be  readily  divided  into  zones,  passing  first 
along  the  eastern  limb  from  north  to  south,  and  then  along 
the  western  limb  from  south  to  north. 


Flo.  1.— Ketardation  of  rotation  in  different  zones  of  the  sun  as  derived 
from  the  prominence  frequency  in  longitude. 

The  diagrams  on  fig.  1  serve  to  illustrate  the  general  situa- 
tion. Referring  to  fig.  4  of  my  former  paper,"  Synchronous 
Changes  in  the  Solar  and  Terrestrial  Atmospheres,  it  is  noted 
that  the  prominence  maximum  activity  is  central  in  the  zones 
10°  to  30°  and  50°  to  70°  of  each  hemisphere,  and  on- this  ac- 
count it  was  decided  to  subdivide  the  solar  disk  into  20-degree 

zones,  as  follows:  -f  90°  to  +  70°,  +  70°  to  +  50°, 

_  50°  to  —  70°,  and  —  70°  to  —  90°,  as  indicated.  A  scale 
was  prepared  which  when  laid  upon  the  published  drawing  of 
a  given  date  would  readily  subdivide  it  into  these  zones  on 
each  side  of  the  sun's  limb. 

For  the  sake  of  recording  the  relative  energy  of  the  solar 

11  Monthly  Weather  Review,  January,  1903,  Vol.  XXXI,  p.  17. 


output  as  registered  in  the  prominences,  a  scale  of  estimation 
was  adopted,  as  follows: 

0  =  an  undisturbed  limb  for  the  zone. 

1  =  a  minor  disturbance. 

2  =  a  somewhat  extensive  disturbance. 

3  =  a  disturbance  pronounced  in  altitude  or  along  a  con- 
siderable extent  of  the  zone. 

4  =  a  very  large,  emphatic  agitation  of  the  limb. 

5  =  the  largest  prominences,  occurring  but  rarely. 

The  state  of  the  limb  was  thus  expressed  in  numbers  of 
relative  energy  by  estimation,  care  being  exercised  to  make  a 
similar  relative  number  do  duty  whenever  the  style  of  the 
drawing  changed  from  one  draftsman  to  another.  The  com- 
putation sheets  were  arranged  to  allow  the  data  for  each  of 
the  nine  zones  to  be  collected  together  by  years  for  the  first 
compilation.  For  the  second  compilation  the  data  belonging 
to  the  same  zone  for  the  successive  years  were  brought  to- 
gether. Hence,  the  work  of  tabulating  the  data  was  repeated 
twice  throughout  the  series.  For  an  ephemeris  I  used  the 
one  already  constructed  from  my  computation  on  the  variations 
of  the  terrestrial  magnetic  field,  having  the  period  26.679  days 
and  epoch  June  13.72,  1887,  as  given  on  page  120,  Bulletin 
No.  21,  Solar  and  Terrestrial  Magnetism.  This  is  known  to 
coincide  very  closely  with  the  period  of  the  solar  rotation  at  the 
equator,  and  as  it  was  one  purpose  of  this  research  to  test  prac- 
tically the  working  of  this  period,  it  was  laid  at  the  basis  of 
the  compilation.  It  makes  no  difference  what  ephemeris  and 
period  are  adopted,  since  any  periodic  phenomenon  not  falling 
upon  that  period  will  show  a  gradual  departure  from  it  by 
the  trailing  of  the  numbers  on  the  sheet  from  left  to  right,  if 
the  period  is  too  short,  or  from  right  to  left,  if  it  is  too  long. 

An  example  of  the  use  of  the  ephemeris  and  the  result  is  given 
in  Table  1.  One  point  should  be  especially  noted  in  this  con- 
nection, and  that  is  as  follows :  The  same  meridian  of  the  sun  is 
seen  twice  in  a  single  rotation,  first  as  the  eastern  limb,  and  second, 
thirteen  days  later,  as  the  western  limb.  Whatever  may  be  the 
intrinsic  activity  of  the  sun  at  a  given  zone  and  on  a  given 
meridian,  that  display  becomes  visible  twice,  first  to  the  east 
and  second  to  the  west.  During  the  passage  of  that  meridian 
across  the  sun's  disk  the  record  is  wanting  so  far  as  this  series 
is  concerned,  though  it  could  of  course  be  studied  otherwise 
by  means  of  the  spectro-heliographic  photographs.  Thus,  as 
the  successive  meridians  come  to  the  edge  of  the  disk,  their 
output  is  recorded  on  the  respective  drawings.  When  these 
are  collated  with  the  equatorial  period,  whatever  characteris- 
tics they  may  have  which  would  imply  special  centers  of  solar 
activity  will  gradually  emerge  upon  the  numerical  tables.  As 
it  is  not  possible  to  reproduce  these  extensive  tables  in  this 
connection,  two  specimens  of  the  second  collection  are  shown 
on  Table  1  for  the  years  1891  and  1892  in  succession,  and  for 
the  zones  +50°  to  +70°  and  +10°  to  +30°.  Imagine  that 
similar  tables  for  zones  +50°  to  +70°  extend  from  1871  to 
1900,  inclusive,  except  for  the  gap  from  1878-1883,  arranged 
continuously  so  that  the  prominence  concentration  and  deple- 
tion flows  without  break  on  the  sheet  from  year  to  year.  This 
process  is  extended  to  the  9  zones,  each  20°  in  width.  In  the 
first  collection  of  the  data  the  highest  number  was  5,  and  this 
was  very  rarely  entered.  Since  the  same  area  on  the  sun  is 
seen  twice,  there  may  be  two  entries  within  the  same  tabular 
area  on  the  first  set  of  sheets.  In  the  second  set  of  sheets  these 
numbers  are  added  together  and  entered  as  one,  so  that  occa- 
sionally the  figures  6,  7,  8  occur,  as  in  Table  1.  They  repre- 
sent the  largest  disturbance  occurring  in  one  small  area  of 
the  sun,  as  defined  by  the  latitude  and  longitude  thus  pre- 
scribed. If  now  the  maxima  show  a  tendency  to  trail  across 
the  sheet  as  indicated  by  the  continuous  lines  drawn  athwart 
the  table,  instead  of  being  scattered  at  random,  then  this  is 
evidence  that  the  center  of  eruption  itself  rotates  about  the 
sun  at  a  different  rate  from  that  laid  down  in  the  assumed 


TABLE  I.  — The  prominence  energy  in  zones  as  collected  on  the  26.68-day  period,  showing  retardation  in  different  latitudes. 


Period  26.67&daiss,.  JZpocA  June  13.  72,  1887. 

Zone  +  6O  °  to  +  7O°. 

7 

2 

3 

4 

5 

6 

7 

8 

ff 

10 

11 

12 

13 

]4 

15 

16 

17 

18 

10 

20 

21 

22 

23 

24 

26 

26 

27 

18.91 

'Jan.  11 

1 

3 

Q 

1 

1 

—  . 

"*-, 

Feb.     6 

2 

/ 

1 

2 

2 

2 

4 

o 

2 

4 

4 

<7 

3" 

•^ 

.2 

2 

Jtfch.    3 

,? 

— 

^4 

3 

2 

1 

2 

^^ 

•^^ 

v4pr:      1 

4 

2 

~~S-~ 

-•— 

4 

3 

2 

1 

1 

1 

2 

2 

/ 

Jlpr.   27 

S> 

•  

>£, 

/ 

2 

1 

<Ma.it  24 

6 

2 

1 

T* 

•^ 

,? 

s 

3 

2 

1 

1 

1 

/ 

Jujie2O 

7 

1 

/ 

5 

2^ 

•#- 

^ 

6 

3 

1 

5 

1 

J 

? 

3 

Jultf  17 

8 

1 

2 

3 

2 

?  " 

^t- 

,£ 

3 

1 

1 

2 

1 

1 

1 

1 

7 

2 

2 

«4W  12 

,9 

/ 

1 

2 

4 

^~ 

-4. 

4 

5 

4 

S 

4 

4 

3 

1 

J 

1 

Seja     8 

JO 

1 

2 

6 

7 

8 

6 

4 

6 

4 

1 

1 

2 

£ 

3- 

J 

7 

7 

6 

3 

4 

3 

3 

3 

Oct.    4 

11 

4 

2 

3 

4 

3 

4 

3 

1 

3 

4 

4 

8 

3 

6 

3 

4" 

•*~ 

J 

8 

3 

3 

7 

4 

2 

1 

Oct   31 

12 

4 

5 

4 

2 

1 

2 

3 

3 

3 

3 

3 

4 

^ 

•-•^, 

3 

4 

JVbr.27 

IS 

2 

/ 

2 

2 

2 

4 

4 

4 

3 

4 

3 

1 

2 

2 

2 

1 

> 

•»-, 

2 

16 

Dec.  23 

/4 

7 

2 

3 

7 

J 

7 

^ 

f> 

/ 

^**n» 

•  —  . 

1892. 

Jan.  79 

1 

1 

2 

1 

1 

2 

2 

1 

S 

3 

J 

1 

1 

1 

1 

Fed.  15 

2 

4 

1 

2 

3 

1 

4 

J 

2 

3 

2 

.Mch.12 

3 

-9- 

•3 

3 

2 

1 

2 

3 

2 

3 

4 

2 

2 

2 

/ 

1 

1 

2 

2 

/ 

2 

4 

17 

JJpr.    8 

4 

6 

6 

V 

-^ 

4 

3 

3 

1 

1 

1 

4 

S 

2 

1 

3 

2 

3 

1 

6 

3 

S 

2 

tACair  £ 

S 

3 

1 

2 

3 

iT 

-~  —  , 

^ 

2 

4 

3 

3 

3 

2 

3 

3 

] 

J 

2 

2 

3 

tMay  31 

6 

1 

2 

2 

2 

3 

3 

"9- 

-^ 

4 

6 

5 

2 

4 

1 

1 

4 

3 

3 

3 

o 

J 

1 

J 

1 

2 

June  27 

7 

4 

3 

2 

1 

2 

2 

3 

3 

3^ 

-#- 

•2 

3 

7 

1 

3 

2 

S 

6 

5 

2 

4 

2 

1 

Jiziv  24 

8 

3 

1 

1 

3 

2 

1 

5 

3 

4 

1r- 

>^ 

4 

4 

6 

3 

4 

3 

2 

3 

2 

3 

2 

^9ucr.J9 

9 

3 

3 

J 

/ 

1 

2 

2 

4 

1 

s 

S 

£- 

•*> 

4 

4 

4 

4 

4 

2 

2 

2 

3 

1 

jSejo.   IS 

1O 

4 

3 

3 

1 

2 

1 

1 

i 

5 

3 

4 

3" 

T- 

f" 

4 

1 

1 

1 

1 

Oct.  12 

11 

3 

3 

1 

1 

5 

4 

2 

2 

1 

2 

J 

2 

3 

5 

2 

^ 

**. 

•3 

1 

2 

2 

6 

JVbir     7 

12 

6 

3 

1 

2 

3 

1 

2 

2 

3 

6 

3 

3 

4 

•y- 

~~~. 

6 

4 

3 

Dec.    4 

13 

3 

3 

3 

4 

2 

2 

2 

2 

2 

2 

•"•-. 

•  —  . 

Zon  e  +JO  °toi-3O  °. 

1891 

Jan    11 

1 

J 

2 

2 

S 

3^ 

^ 

2 

2 

/ 

/ 

14 

Feb     6 

2 

X 

5 

2 

1 

/ 

1 

I 

I 

/ 

2 

2 

1 

^ 

(,/ 

/ 

2 

I 

I 

J 

4 

3 

/ 

Jtfch    5 

3 

2 

^. 

1 

1 

2 

1 

6 

6 

X 

6 

3 

2 

2 

,j3pr*.     1 

4 

1 

^\ 

s? 

1 

3 

2 

4 

3 

I 

1 

2 

I 

I 

/ 

"^ 

2 

2 

r 

tApr.  27 

S 

1 

7s 

V 

8 

1 

3 

2 

1 

3 

/ 

; 

*x 

1 

3 

J 

I 

f 

3 

1 

<Mav  24 

& 

1 

/ 

2s 

^2 

1 

1 

4 

1 

I 

S 

8 

2 

/ 

g 

3 

S? 

4 

3 

4 

/ 

4 

.5- 

2 

June  2O 

7 

3 

3 

3 

2 

N 

/ 

3 

4. 

3 

7 

3 

7 

3 

/ 

2 

N? 

2 

3 

2 

3 

,-i 

July   11 

8 

3 

5 

1 

2 

7 

X 

2 

6 

4 

4 

2 

1 

3 

4 

S 

5 

/ 

V 

S 

2 

4 

vfuer.  12 

9 

4 

4 

6 

4 

3 

3 

V 

2 

/ 

2 

2 

2 

1 

5 

3 

4 

7 

/ 

S 

s/ 

2 

5 

3 

Set,    8 

10 

4 

3 

5 

4 

,5 

4 

«?' 

N? 

2 

2 

1 

3 

3 

2 

2 

/ 

X 

4 

5 

Oct.    4 

11 

2 

4 

1 

3 

1 

2 

\ 

•x? 

1 

2 

J 

1 

7 

3 

/ 

/ 

X 

7 

Oct   31 

12 

2 

1 

2 

3 

2 

x 

y? 

4 

J 

2 

/ 

4 

\ 

JVor.27 

13 

I 

7 

4 

3 

2s 

/ 

/ 

2 

4 

2 

4 

4 

2 

/ 

2 

X 

Dec.  23 

14 

/ 

2 

2 

2 

\ 

2 

I 

7 

/ 

2 

fi 

3 

? 

7 

7' 

\ 

1892 

Jasi   19    ' 

i 

1 

2 

2 

2 

3 

X 

2 

4 

1 

2 

4 

4 

2 

1 

Feb   15 

2 

2 

1 

2 

7 

5 

4 

V 

4 

1 

2 

4 

3 

3 

3 

<MchJ2 

3 

2 

1 

3 

3 

1 

3 

3 

3 

£' 

« 

,? 

S 

2 

2 

7 

<df>r.     8 

4 

1 

2 

6 

5 

3 

2 

1 

4 

3 

/ 

V 

s 

7 

2 

4 

4 

3 

7 

Jfyfcti/  5 

A' 

X 

2 

J 

3 

1 

\ 

^2 

J 

3 

7 

7 

f) 

7 

s. 

,5 

*A£aif3J 

6' 

5 

\ 

1 

3 

2 

2 

3 

4 

3 

2 

3 

4 

X 

3 

P. 

3 

?, 

3 

g 

7 

7 

June  27 

7 

3 

6^ 

^ 

1 

4 

/ 

6 

/ 

2 

4 

3 

4 

,5 

.? 

2 

X 

I 

7 

2 

2 

3 

3 

G 

?, 

3 

7 

July  24 

y 

1 

4 

2\ 

/ 

3 

4 

2 

I 

4 

2 

3 

4 

f 

4 

^ 

3 

?! 

7 

,? 

,? 

e 

3 

ttfitff.ld 

9 

4 

4 

3 

*s, 

2 

! 

3 

/ 

2 

3 

2 

3 

4 

2 

3 

6 

V 

?. 

7 

7 

ft 

1 

4 

Sep.  15 

10 

2 

2 

3 

3 

\ 

3 

3 

1 

7 

7 

4 

7 

3 

5 

4 

7s 

V? 

?, 

,f 

3 

,? 

?. 

7 

Oct  12 

11 

3 

2 

J 

2 

s? 

2 

I 

3 

3 

7 

3 

3 

4 

2 

,? 

? 

e 

I 

g 

,f 

JVbv.   7 

12 

3 

1 

% 

^ 

3 

1 

4 

2 

1 

/ 

7 

4 

6 

4 

E 

.6 

S 

f 

Dec.    4 

13 

2 

4 

5 

5 

2 

I 

2\ 

J. 

/ 

2 

?, 

7 

2 

3 

7 

2 

f> 

Si 

9 

16 

"VT 

ephemeris.  From  such  trails  the  angular  retardation  in  dif- 
ferent zones  can  be  computed  with  considerable  exactness. 
The  reader  will  not  receive  a  satisfactory  impression  of  the 
distinctness  with  which  this  trailing  at  different  rates  in  the 
several  zones  occurs,  without  an  inspection  of  the  entire  series 
of  tables,  and  it  is  hoped  that  they  will  be  published  in  a 
special  report,  as  the  subject  matter  is  evidently  very  im- 
portant and  suggestive  for  the  solution  of  the  fundamental 
problem  of  the  mode  of  the  internal  solar  circulation. 

An  examination  of  these  sheets  indicates  that  there  is  a 
marked  tendency  for  the  numbers  to  bunch  themselves  to- 
gether in  a  very  special  manner.  Between  the  successive  years 
there  is  generally  a  depletion  corresponding  with  the  winter 
months,  while  the  summer  months  are  relatively  full  and  com- 
plete. As  pointed  out  in  my  paper  on  Synchronous  Changes, 
this  is  evidently  due  to  the  fact  that  the  relatively  cloudy 
weather  in  Italy  during  the  winter  months  made  it  impossible 
to  secure  so  many  days  of  observation  as  during  the  summer, 
and  I  conclude  that  the  apparent  concentration  of  the  tables 
in  the  summer  season  is  a  meteorological  effect,  and  should  be 
treated  as  such  in  interpreting  the  results.  At  the  same  time 
there  is  a  very  similar  concentration  of  the  numbers  along  the 
days  of  the  period,  corresponding  with  a  solar  rotation,  which 
can  not  be  explained  in  that  way,  since  it  occurs  as  prominently 
in  summer  as  in  winter.  It  must  apparently  be  referred  back 
to  some  solar  activity  producing  prominences  on  the  two  op- 
posite sides  of  the  sun.  The  maximum  numbers  not  only  trail 
downwards  and  to  the  right  on  the  tables,  but  the  lines  of  maxi- 
mum also  drift  across  the  tables  to  the  left,  thus  indicating 
retardation  in  the  higher  latitudes  relative  to  the  adopted 
equatorial  period. 

It  may  be  mentioned  in  passing  that  this  increase  of  activity 
of  the  sun  on  two  opposite  sides  of  its  mass,  as  if  a  certain 
diameter  had  greater  energy  than  the  one  at  right  angles  to 
it,  has  already  been  detected  by  me  in  the  meteorological  field 
of  the  earth's  atmosphere,  and  also  in  the  terrestrial  magnetic 
field,  as  shown  on  pages  91  and  92  of  my  Eclipse  Meteorology 
and  Allied  Problems,  and  elsewhere.  This  persistent  excess 
of  outflowing  energy  on  two  opposite  sides  of  the  sun  suggests 
the  possibility  that  the  sun  should  be  regarded  as  an  incipient 
binary  star,"  where  the  dumbbell  figure  of  revolution  prevails 
instead  of  the  spheroidal.  If  this  is  really  the  case,  and  the 
evidence  suggests  it,  then  there  would  be  a  reason  for  the 
existence  of  the  two  primary  centers  of  activity  in  the  sun, 
instead  of  its  having  a  single  center.  Some  double  acting 
system  appears  to  impress  itself  generally  upon  the  solar  cos- 
mical  relations.  From  this  we  should  expect  to  find  that  the 
sun  has  two  magnetic  and  two  meteorological  systems,  inter- 
acting so  as  to  form  the  configuration  of  the  external  field  as 
measured  at  the  earth.  There  would  then  be  sufficient  ground 
for  a  differential  action  in  the  terrestrial  pressures  and  temper- 
atures, as  detected  in  the  discussion  of  such  data  by  many 
students. 

This  view  is  quite  in  harmony  with  the  well  known  fact  of 
the  existence  of  numerous  binary  systems  of  suns  more  or  less 
widely  separated,  and  it  can  not  be  regarded  as  unlikely  that 
the  sun  is  actually  developing  in  this  way.  The  enormous 
mass  of  the  sun  would  seem  to  entice  its  constituents  to  group 
themselves  preferably  about  two  centers  for  the  physical  pro- 
cesses involved  in  circulation  and  radiation,  rather  than  about 
one,  and  I  suspect  that  this  is  the  correct  explanation  of  sev- 
eral well  known  phenomena. 

DISCUSSION    OF    THE    OBSERVATIONS. 

On  Table  1  are  given  some  examples  of  the  slope  of  the  line 
of  maximum  frequency  numbers  in  successive  years.  These 

11  Compare  Figures  of  Equilibrium  of  Eotating  Masses  of  Fluids.  By 
G.  H.  Darwin,  Proc.  Roy.  Soc.  Vol.  XLII.  1887,  p.  359.  Thomson  and 
Tait,  Nat.  Phil.  Vol.  I,  part  2,  pp.  330-335. 


were  drawn  originally  by  a  careful  examination  of  the  entire 
set  of  figures,  and  an  effort  was  made  to  locate  the  line  along 
the  maximum  numbers  so  as  to  balance  as  nearly  as  possible 
the  entire  system  on  either  side  of  it.  Some  regard  was  paid 
to  the  average  trend  of  the  lines  in  the  other  portions  of  the 
same  zone,  whereby  one's  judgment  was  guided  in  cases  of 
doubt.  Entire  impartiality  was  exercised  as  far  as  practicable, 
and  the  results  now  about  to  be  described  were  entirely  un- 
expected. It  would  perhaps  be  preferable  to  utilize  least 
square  methods,  if  one  could  afford  so  great  labor.  The  lines 
are  all  numbered,  as  16,  17  in  the  zone  +  50°  to  +  70°, 
which  are  complete;  those  in  zone  +  10°  to  -f  30°,  namely 
14,  15,  16,  are  fragmentary  on  Table  1.  We  now  count 
the  number  of  days  which  have  elapsed  for  a  certain  number 
of  periods,  in  order  to  find  the  average  rate  of  retardation  per 
rotation  of  26.68  days.  Thus,  for  the  line  16,  zone  +  50° 
to  -f  70°,  about  12  periods  elapsed,  beginning  with  period  2 
and  ending  with  period  14,  while  the  line  was  trailing,  or  the 
period  was  retarded,  26.7  days.  Hence,  26.7 -=- 12  =  2.225 
days  retardation  per  period  of  26.68  days,  so  that  the  rotation 
period  in  that  zone  is  28.905  days.  Similarly,  line  17  gives  a 
retardation  of  26. 2  days  in  11  periods.  Hence,  26.2  -4-  11  =  2.382. 
These  two  values  are  entered  in  the  proper  place  on  Table  2. 
The  results  have  been  grouped  by  years  where  the  solar  energy 

TABLE  2. — Retardation  of  the  sun  in  different  latitudes  as  derived  from  the 
prominence  frequency  in  longitude,. 


Years. 

Slope. 

OJ 

3 
A 

Periods. 

CO 

£ 

ft 

Retarda- 
tion. 

d 

i 

3 

Periods. 

IK 

:>> 

s 
ft 

Retarda- 
tion. 

1871-1877 
1884-1888 
1889-1893 
1894-1900 

Max.-Min. 
Max.-Min. 
Min.-Max. 
Max.-Min. 

Zone  +  10°  to  —  10°. 

1 

2 
3 

4 
5 
6 

7 
8 

90 
90 
69 
69 
68 
68 
96 
69 

9.0 
9.0 
6.5 
7.4 
5.2 
6.0 
11.4 
8.2 

0.100 
0.100 
0.094 
0.107 
0.077 
0.088 
0.119 
0.119 

Me 

in  ... 

0.101 

1871-1877 

1884-1888 

1889-1893 
1894-1900 

Max.-Min. 

Max.-Min. 

Min.-Max. 
Max.-Min. 

Zone  -f  10°  to  +  30°. 

Zone  —  10°  to  —  30°. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 

18 
41 
39 
35 
25 
26 
9 
19 
34 
35 
35 
10 
18 
31 
31 
23 
33 
37 
35 
34 
28 

12.8 
28.2 
26.1 
25.3 
20.2 
17.8 
6.0 
14.0 
26.0 
26.0 
25.0 
7.2 
16.2 
26.7 
26.2 
19.0 
26.3 
26.7 
27.8 
26.6 
20.7 

0.711 
0.688 
0.  669 
0.723 
0.808 
0.684 
0.666 
0.737 
0.765 
0.743 
0.714 
0.720 
0.  900 
0.863 
0.845 
0.826 
0.797 
0.722 
0.794 
0.783 
0.739 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 

15 
28 
38 
39 
37 
26 
10 
16 
31 
33 
35 
17 
16 
34 
34 
27 
33 
35 
34 
36 
35 
34 
13 

12.5 
22.1 
26.5 
27.0 
27.0 
19.0 
7.3 
14.0 
27.0 
26.7 
26.5 
14.0 
13.6 
26.8 
26.7 
22.0 
26.4 
27.0 
26.6 
28.0 
26.8 
24.0 
9.8 

0.833 
0.789 
0.  697 
0.  692 
0.729 
0.731 
0.  730 
0.875 
0.873 
0.809 
0.803 
0.824 
0.  850 
0.788 
0.785 
0.815 
0.800 
0.722 
0.783 
0.  778 
0.  766 
0.  706 
0.753 

Mei 

in  

0.757 

Mes 

in  .  . 

0.782 

. 


TABLE  2. — Retardation  of  the  sun  in  different  latitudes  as  derived  from  the 
prominence  frequency  in  longitude — Continued. 


Years. 

Slope. 

<o 

a 

3 

Periods. 

CO 

E? 
O 

Retarda- 
tion. 

® 

c 

3 

Periods. 

CO 

1 

0 

Ketarda- 
tion. 

1871-1877 

1884-1888 
1889-1893 
1894-1900 

Max.-Min. 

Max.-Min. 
Min.-Max. 
Max.-Min. 

Zone  +  30°  to  +  50°. 

Zone—  30°  to  —50°. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 

15 
20 
20 
19 
18 
18 
24 
21 
20 
21 
22 
23 
21 
19 
22 
23 
24 
24 
25 
26 
27 
26 
30 
35 
28 
27 

21.0 
27.0 
27.4 
28.0 
27.4 
27.3 
33.0 
25.3 
24.2 
27.0 
27.2 
27.5 
27.5 
26.0 
27.0 
27.0 
27.0 
27.5 
27.7 
27.0 
27.4 
27.0 
27.0 
26.5 
26.2 
23.8 

1.400 
1.350 
1.370 
1.474 
1.522 
1.517 
1.375 
1.205 
1.210 
1.  286 
1.236 
1.196 
1.309 
1.368 
1.227 
1.174 
1.125 
1.146 
1.108 
1.038 
1.015 
1.038 
0.900 
0.786 
0.936 
0.881 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 

18 
26 
27 
25 
24 
27 
24 
10 
15 
28 
27 
32 
29 

19.8 

27.0 
26.4 
27.3 
26.7 
27.7 
24.6 
9.9 
14.5 
26.0 
23.6 
27.2 
27.2 

1.100 
1.038 
0.978 
1.092 
1.112 
1.026 
1.025 
0.990 
0.967 
0.929 
0.874 
0.850 
0.938 

14 
15 
16 
17 
18 

28 
29 
32 
27 
26 

27.0 
27.8 
27.2 
27.2 
26.0 

0.964 
0.958 
0.850 
1.007 
1.000 

19 
20 
21 
22 
23 
24 

30 

29 
23 
25 
29 
30 

27.8 
27.2 
26.0 
27.0 
28.0 
27.0 

0.927 
0.938 
1.130 
1.080 
0.965 
0.900 

Me 

in  

1.192 

Me 

in 

0.989 

1871-1877 

1884-1888 
1889-1893 

1894-1900 

Max.-Min. 

Max.-Min. 
Min.-Max. 

Max.-Min. 

Zone  +  50°  to  +  70°. 

Zone  —  50°  to  —  70°. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 

13 
13 
14 
11 
13 
15 
19 
8 
18 
18 
21 
19 
14 
14 
15 
12 
11 
13 

27.7 
27.0 
27.0 
27.3 
27.5 
27.0 
27.3 
14.0 
27.7 
28.0 
27.6 
27.3 
27.7 
27.7 
27.4 
26.7 
26.2 
28.0 

2.131 

2.077 
1.928 
2.482 
2.115 
1.800 
1.437 
1.750 
1.539 
1.556 
1.314 
1.437 
1.979 
1.979 
1.827 
2.225 
2.382 
2.154 

1 
2 
3 

4 
5 
6 

7 

11 
15 
13 
12 
15 
15 
9 

20.6 
26.6 
27.0 
27.0 
27.4 
26.8 
19.0 

1.873 
1.773 
2.077 
2.250 
1.827 
1.787 
2.111 

8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

10 
10 
12 
13 
11 
11 
12 
11 
11 
11 
12 
13 
11 
10 
11 
15 
18 
17 

26.0 
26.2 
27.8 
26.4 
26.5 
26.0 
26.6 
27.8 
27.0 
26.4 
27.5 
26.0 
27.0 
27.5 
27.0 
26.4 
27.6 
27.7 

2.600 
2.620 
2.317 
2.031 
2.409 
2.364 
2.217 
2.527 
2.455 
2.400 
2.292 
2.000 
2.455 
2.750 
2.455 
1.760 
1.533 
1.629 

19 
20 
21 
22 
23 
24 
25 

15 
13 
9 
10 
10 
11 
12 

27.0 
27.0 
26.0 
27.4 
27.5 
27.5 
27.0 

1.800 
2.769 
2.  889 
2.740 
2.750 
2.500 
2.250 

Mes 

in  

2.072 

Mes 

in 

2.180 

is  passing  from  maximum  to  minimum,  1871-1877,  1884-1888, 
1894-1900,  and  again  where  it  is  passing  from  minimum  to 
maximum  (1878-1883,  lacking),  1889-1893,  so  as  to  study  the 
effect  of  this  variation  in  the  retardation;  but  the  unfortunate 
gap  1878-1883  prevents  a  satisfactory  comparison  between 
these  two  groups.  The  several  zones  are  given  separately  for 


each  hemisphere,  and  the  successive  trails  can  be  readily  scru- 
tinized. 

The  first  column  of  Table  2  contains  the  years  of  the  groups; 
the  second  the  slope  of  the  11-year  curve,  roughly;  the  third 
the  number  of  the  line  in  the  zone ;  the  fourth  the  number  of 
periods  elapsed;  the  fifth  the  number  of  days  of  retardation 
in  these  periods;  the  sixth  the  average  retardation  in  days  on 
the  26.68-day  period.  The  mean  retardation  for  each  zone  in 
both  hemispheres  is  given,  and  has  been  collected  in  Table  3. 
It  was  necessary  to  assume  that  the  mean  latitude  of  the  oc- 
currence of  the  prominences  is  in  the  middle  of  each  zone, 
though  this  can  not  be  strictly  correct.  It  would  require 
very  extensive  computation  to  determine  the  mean  latitude  of 
occurrence  of  the  several  zones  more  accurately.  The  aspect 
of  the  path  of  maximum  frequency  as  given  on  fig.  4  of  my 
previous  article  entitled  Synchronous  Changes,"  is  favora- 
ble to  this  simple  assumption. 

TABLE  3. — Mean  retardation  by  zones. 


Mean 

latitude. 

Eetardatlon. 

Mean 
period. 

North. 

South. 

Mean. 

o 
0 
5 
20 
40 
60 

0.000 
0.101 
0.757 
1.192 
2.072 

0.000 
0.101 
0.782 
0.989 
2.180 

0.000 
0.101 
0.770 
1.091 
2.126 

26.68 
26.78 
27.45 
27.77 
28.81 

TABLE  4. — Bigelow's  rotation  periods. 


Latitude. 

Daily 
angular 
velocity. 

Sidereal 
period. 

Synodic 
period. 

o 

• 

Days. 

Days. 

Pole  90 

788 

27.40 

29.63 

85 

790 

27.32 

29.54 

80 

793 

27.23 

29.43 

75 

795 

27.15 

29.33 

70 

799 

27.03 

29.18 

65 

804 

26.86 

29.00 

60 

809 

26.70 

28.81 

II  Pr.  55 

815 

26.50 

28.58 

50 

824 

26.20 

28.23 

45 

832 

25.94 

27.93 

40 

837 

25.81 

27.77 

35 

840 

25.71 

27.66 

30 

842 

25.66 

27.60 

25 

845 

25.57 

27.50 

I  Pr.  20 

846 

25.53 

27.45 

15 

852 

25.36 

27.26 

Spots  10 

859 

25.15 

27.00 

5 

866 

24.95 

26.78 

Equator    0 

869 

24.86 

26.68 

A  careful  examination  of  the  individual  determinations  of 
the  retardations  in  the  several  zones  shows  that  there  is  a 
wide  fluctuation  which  increases  in  magnitude  from  the  equa- 
tor toward  the  poles.  In  order  to  obtain  a  clear  idea  of  the 
law  of  the  retardations  these  results  have  been  plotted  on 
fig.  2. 

The  mean  retardation,  with  an  approximate  maximum  and 
minimum  retardation,  is  there  indicated.  From  the  mean  line 
I  have  scaled  off  the  corresponding  synodic  periods  for  every 
five  degrees  of  latitude,  as  given  in  Table  4,  and  have  computed 
the  sidereal  period  and  the  daily  angular  velocity,  X,  in  minutes 
of  arc  belonging  to  them.  These  transformations  can  readily 
be  made  by  interpolations  from  Table  5. 

"Monthly  Weather  Beview,  January,  1903,  Vol.  XXXI,  p.  17. 


6 


The  latitude  at  which  the  maximum  of  spots  is  commonly 
observed,  and  also  the  latitude  of  the  maxima  I  and  II  of 
prominence  frequency,  are  indicated  in  Table  4  and  fig.  2  by 
the  terms  "  Spots,"  "  I  Pr.,"  "  II  Pr." 

TABLE  5.— Transformations  of  the.  daily  angular  velocity  into  sidereal  and 

synodic  periods. 
T=sidereal  period  of  the  sun;  £=sidereal  period  of  the  earth;  5=sj'nodic  period  of  the 

sun.     Then  we  have  ~    ~~~    ~"~ "' 


Daily  X 

T 

1_ 

1_ 

1 

~S 

a 

900 

24.00 

0.  04167 

0.  00274 

0.  03893 

25.69 

895 

24.13 

0.  04144 

0.  03870 

25.84 

890 

24.27 

0.  04120 

0.  03846 

26.00 

885 

24.41 

0.  04097 

0.  03823 

26.16 

880 

24.55 

0.  04074 

0.03800 

26.32 

875 

24.69 

0.04051 

0.  03777 

26.48 

870 

24.83 

0.  04028 

0.  03754 

26.64 

865 

24.97 

0.04005 

0.03731 

26.80 

860 

25.12 

0.  03982 

0.  03708 

26.97 

855 

25.26 

0.03958 

0.  03684 

27.14 

850 

25.41 

0.  03935 

0.03661 

27.32 

845 

25.56 

0.  03912 

0.  03638 

27.49 

840 

25.71 

0.  03889 

0.  03615 

27.66 

835 

25.87 

0.03867 

0.  03592 

27.84 

830 

26.02 

0.  03843 

0.  03569 

28.01 

825 

26.18 

0.03819 

0.  03545 

28.21 

820 

26.34 

0.  03796 

0.  03522 

28.39 

815 

26.50 

0.  03773 

0.  03499 

28.58 

810 

26.67 

0.  03750 

0.  03476 

28.77 

805 

26.83 

0.  03727 

0.  03453 

28.96 

800 

27.00 

0.  03704 

0.  03430 

29.15 

795 

27.17 

0.  03681 

0.  03407 

29.35 

790 

27.34 

0.  03657 

0.  03383 

29.56 

785 

27.52 

0.03634 

0.  03360 

29.76 

Latitude, 
so 

4(? 
70' 
60° 

so" 

40 
'30 
SO 

10 
g 

J-. 

^ 

// 

1 
1 

&''  ,.* 

2 

/ 
/ 

/ 

J 

w^' 

^ 

/ 
/ 

,/ 

JLProm. 

nences 

.''     fe<> 

^^ 

--""M"3 

fl 

/ 
/ 

^ 

&£. 

eta1"*" 

I 

!  / 

'','& 

c1' 

LProjnin 

/  7 

*na€f    , 

/ 
/ 

Spots^. 

¥"'' 

/' 

Rftartt'n 

?            a 

50             J 

TO               1 

50            2 

w          2 

50             3 

OOdaj-s 

KrixfZS 

68          27 

1.1          27 

G8            26 

/a       zs 

SS         29 

/S           29 

fiSdayS. 

FIG.  2. — Periods  of  rotation  of  the  solar  photosphere  derived  from  the 
prominence  frequency  in  different  zones. 

It  should  be  noted  that  the  mean  retardation  does  not  fol- 
low a  regular  slope,  or  a  simple  curve  that  can  be  reduced  to  an 
analytic  function.  From  latitude  20°  to  40°  there  is  a  smaller 
inclination  than  on  the  slopes  between  0°  and  20°,  or  on  those 
between  40°  and  60°.  In  fig.  2  the  line  has  been  extended 
to  90°,  that  is  to  the  pole,  but  it  is  unknown  beyond  70°,  since 
the  polar  zones  were  too  irregular  to  permit  any  use  of  this 
method.  It  is  probable,  that  a  continuous  line,  as  indicated,  is 
nearly  correct. 

In  order  to  compare  my  result  with  some  well  known  rota- 
tion periods,  (taken  conveniently  from  Miss  Clerke's  Problems 
in  Astrophysics,  p.  146),  the  following  compilation  is  intro- 
duced: 


Heliographic 
latitude. 

Spots. 

Prominences. 
(Bigelow). 

Faculee. 

0 

0 

25.09 

24.  86 

24.66 

15 

25.44 

25.  36 

25.26 

30 

25.81 

25.66 

25.48 

From  this  it  appears  that  my  prominence  rotations  lie  mid- 
way between  those  of  the  spots  and  the  faculse.  Duner's  ro- 
tations for  the  reversing  layer,  as  quoted  by  Miss  Clerke,  are 
apparently  impossible.  The  determinations  of  the  rotation 
period  as  given  by  the  well-known  formula)  of  Carrington, 
Spoerer,  Faye,  and  Tisserand  are  found  in  Table  6.  These 
periods  begin  to  depart  from  the  rotations  as  found  from  the 
prominences  after  leaving  the  latitude  of  20°. 

TABLE  6. — Several  denominations  of  the  rotation  periods  of  the  solar  spots 
in  different  latitudes. 


Carrington. 

Spoerer. 

d 

X 

T 

S 

X 

T 

S 

o 

, 

, 

0 

865 

24.97 

26.80 

877 

24.  65 

26.42 

5 

863 

25.03 

26.90 

864 

25.00 

26.83 

10 

857 

25.20 

27.  07 

853 

25.32 

27.21 

15 

849 

25.44 

27.35 

842 

25.65 

27.59 

20 

840 

25.71 

27.66 

833 

25.93 

27.91 

25 

828 

26.08 

28.09 

825 

26.18 

28.21 

30 

816 

26.47 

28.54 

819 

26.37 

28.43 

35 

803 

26.93 

29.04 

814 

26.53 

28.62 

40 

789 

27.38 

29.60 

810 

26.67 

28.77 

Faye. 

Tisserand. 

d 

X 

T 

8 

X 

T 

8 

0 

, 

, 

0 

862 

25.06 

26.90 

858 

25.18 

27.04 

5 

861 

25.  09 

26.93 

857 

25.20 

27.  07 

10 

856 

25.23 

27.11 

853 

25.  32 

27.21 

15 

850 

25.41 

27.  32 

847 

25.50 

27.  42 

20 

840 

25.71 

27.66 

840 

25.71 

27.66 

25 

829 

26.05 

28.05 

830 

26.  02 

28.01 

30 

815 

26.50 

28.58 

819 

26.37 

28.43 

35 

801 

26.97 

29.11 

806 

26.80 

28.92 

40 

785 

27.52 

29.76 

793 

27.24 

29.  43 

It  is  proper  to  remark  that  the  agreement  in  low  latitudes, 
between  the  periods  obtained  from  the  prominences,  the  spots, 
and  the  faculse  is  not  unfavorable  to  a  feeling  of  confidence  in 
the  results  obtained  by  the  prominence  method  in  higher  lati- 
tudes. This  is  perhaps  strengthened  by  the  further  develop- 
ments which  are  indicated  in  the  next  section. 

THE    DIFFERENTIAL    CIRCULATION    WITHIN    THE    SUN. 

In  order  to  study  more  minutely  the  meaning  of  the  fluctua- 
tions in  the  relative  retardations  given  for  successive  lines  in 
Table  2,  it  is  seen  that  we  have  practically  obtained  a  value  of 
the  retardation  for  each  year  of  the  interval  1871-1900,  except 
for  the  gap  1878-1883,  and  that  by  plotting  these  as  ordinates 
on  a  diagram  whose  abscissas  are  the  years,  a  curve  of  relative 
retardation  in  the  several  zones  can  be  constructed.  Fig.  3 
exhibits  these  data  in  a  graphical  form.  Thus,  in  the  northern 
hemisphere,  for  the  zone  -f-  50°  to  +  70°,  the  ordinates  in  Table 

2,  beginning  with  that  for  1871,  read  2.13, 2.08, 1.93, 2.25, 

and  these  form  the  successive  points  of  the  retardation  curve. 


In  the  upper  section  of  the  diagram  marked  "  Prominence  fre- 
quency "  is  reproduced  the  curve  of  average  prominence  fre- 
quency for  the  entire  sun,  which  is  the  mean  curve  of  the  zonal 
system  shown  on  fig.  2  of  my  paper  on  Synchronous  Changes,14 
and  is  also  reproduced  at  the  head  of  fig.  28  of  my  paper,  A  Con- 
tribution to  Cosmical  Meteorology.15  An  inspection  of  the 
curves  of  fig.  3,  shows  plainly  three  important  facts  of  fundamen- 
tal significance:  (1)  the  retardations  relative  to  the  equatorial 
period  of  rotation,  26.G8  days,  increase  toward  the  poles;  (2) 
the  irregularities  in  the  observed  retardations  are  very  much 
greater  in  the  polar  than  in  the  equatorial  zones;  (3)  these 
irregularities  in  the  retardation  do  not  appear  to  be  accidental, 
but  they  synchronize  closely  with  the  variations  in  the  fre- 
quency of  the  prominences.  The  value  of  this  last  inference 
is  very  great,  in  view  of  the  other  facts  brought  out  in  various 
portions  of  my  research.  Using  this  prominence  curve  as  the 
standard  of  reference  we  have  already  proved  the  following 
facts:  (1)  The  elements  of  the  earth's  magnetic  field  fluctuate 
with  it  annually  in  synchronism;  (2)  the  terrestrial  tempera- 
tures and  barometric  pressures  synchronize  with  it,  as  will  be 
shown  conclusively  in  my  next  paper,  in  the  MONTHLY  WEATHER 
EEVIEW  for  November,  1903;  (3)  the  internal  circulations  of 
the  sun,  as  recorded  in  the  rotational  velocities  of  the  photos- 
phere, also  synchronize  with  the  same  curve.  This  exhibit 
binds  the  entire  solar  and  terrestrial  atmospheres  in  one  syn- 
chronous circulation,  and  it  therefore  places  the  entire  subject 
of  cosmical  meteorology  upon  a  satisfactory  basis,  entirely  in 
harmony  with  the  procedure  marked  out  in  previous  papers. 

While  it  can  not  be  supposed  that  this  discussion  of  the 
solar  prominence  frequency  in  longitude  gives  us  final  quanti- 
tative results  on  the  rotation  phenomena  of  various  zones,  yet 
the  line  of  argument  is  sufficiently  sustained  to  warrant  further 
extensions  of  the  research.  We  have  shown  that  the  solar 
angular  velocity  diminishes  from  the  equator  toward  the  poles 
at  a  certain  rate,  as  on  fig.  1  for  example,  or  as  on  fig  4. 

This  is  in  harmony  with  the  von  Helmholtz-Emden  equa- 
tions for  a  rotating  mass  hot  at  the  center  and  cooling  toward 
the  surface.16  In  such  a  mass  there  are  discontinuous  concave 
cylindrical  surfaces  coaxial  with  the  axis  of  rotation,  the  equa- 
torial parts  being  nearer  the  axis  than  are  the  polar  parts. 
This  also  implies  that  the  polar  regions  of  the  sun  are  warmer 
than  the  equatorial  by  reason  of  the  currents  from  the  center 
toward  the  poles.  At  a  surface  of  discontinuity,  on  each  side 
of  which  the  pressure  is  the  same,  but  the  temperature  and 
angular  momentum  different,  as  where  a  rapidly  moving  cur- 
rent flows  over  a  more  slowly  moving  current  in  the  earth's 
atmosphere,  the  conditions  are  favorable  for  forming  vortex 
tubes,  terminating  on  the  surface,  but  extending  through  the 
mass  of  the  sun.  They  are  right-handed  in  the  northern 
hemisphere  and  left-handed  in  the  southern  hemisphere,  for 
convective  actions  from  the  equator  toward  the  poles.  If  vor- 
tices are  thus  formed  in  the  sun,  so  far  as  the  state  of  its  ma- 
terial permits,  then  the  solar  mass  is  in  fact  in  a  polarized 
state,  the  internal  matter  tending  to  rotate  throughout  the 
globe  around  such  lines  as  are  the  generators  of  the  required 
discontinuous  surfaces.  The  turbulent  conditions  of  internal 
circulation  tend  to  a  lawful  disposition  by  the  regulative  action 
of  a  hot  mass  gravitating  to  a  center  by  its  own  internal  forces 
and  emitting  heat  through  these  processes  of  circulation  ac- 
companied by  polarization  and  rotating  vortex  tubes.  The 
contents  of  a  tube  must  be  made  up  of  molecules  and  atoms 
more  or  less  charged  with  electricity,  and  the  necessary  rota- 
tory motion  produces  Amperean  electric  currents  which  are  a 
sufficient  cause  for  the  generation  of  a  true  magnetic  field, 
positive  on  the  northern  and  negative  on  the  southern  hemis- 
phere of  the  sun.  This  conforms  to  the  result  reached  years 

14  Monthly  Weather  Review,  January,  1903,  Vol.  XXXI   p   10 

15  Monthly  Weather  Review,  July,  1902,  Vol.  XXX,  p.  352 

16  See  Eclipse  Meteorology,  pages  70  and  71. 


ago  by  my  analysis  of  the  terrestrial  magnetic  field,  which 
showed  that  the  earth  appears  to  be  immersed  in  a  magnetic 
field  perpendicular  to  the  plane  of  the  ecliptic  and  positive  to 
the  north  of  it.  Variable  circulation  within  the  solar  mass 
would  display  itself  in  corresponding  changes  in  the  rotation 
of  the  discontinuous  surfaces,  in  the  vortices  carrying  electri- 
cal charges,  in  the  external  magnetic  field,  in  the  number  of 
prominences,  faculae,  and  spots,  in  the  earth's  magnetic  and 
electric  fields,  and  in  the  terrestrial  temperatures  and  pres- 
sures. Synchronism  having  thus  been  established  through- 
out this  vast  complex  cosmical  system  and  referred  back  to 
fundamental  thermodyuamic  and  hydrodynamic  laws,  it  be- 
comes possible  to  make  further  advances  in  the  problems  of 
solar  physics.  Thus,  the  curvature  of  the  internal  lines  can 


J870 


J87S 


2.50 


1.50 


JOO 


OSO 


2.SO 


2.00 


0.60 


J88S 


J890 


1S95 


1906 


Northern  Hemisphere. 


Southern  Hemisphere. 


Zone-7O°to-5O: 


Zone-50°to-30. 


Zone-3O°to-JO. 


Zone-lO°toO° 


T 


FIG.  3.— Variable  retardations  in  the  periods  of  rotation  of  the  solar 

photosphere. 


8 


be  studied  in  different  parts  of  the  meridian  section  on  pass- 
ing from  the  surface  of  the  sun  to  internal  parts  by  means  of 
the  vortex  law  of  constant  angular  momenta,  Q  =  u>  va 2,  under 
the  assigned  thermal  conditions.  We  shall  make  an  attempt 
to  do  this  in  a  report  which  will  contain  the  tabular  data  in 
full  upon  which^ these  deductions  are  based. 

If  it  is  true  that  large  cosmical  cooling  masses  in  rotation 


N  Pole. 


S  Pole. 


FIG.  4. — Formation  ol  vortices  in  the  solar  mass  by  differential  rota- 
tions. 


contain  u  polarized  or  vortical  internal  structure  which  is  the 
basis  of  a  magnetic  field,  then  it  follows  that  this  is  the  ex- 
planation of  the  earth's  magnetism  as  well  as  of  the  magnetism 
of  the  sun.  Hence,  all  stars  are  magnetized  spheres,  and  their 
relative  magnetism  would  be  a  measure  of  the  activity  of  their 
internal  circulations.  Thus,  the  relative  intensity  of  the  earth's 
and  the  sun's  magnetization  becomes  a  measure  of  the  internal 
vortical  circulation  in  polarized  tubes,  and  the  variations  of 
the  earth's  magnetic  field  have  a  cosmical  significance,  not 
only  as  to  the  direct  action  of  the  sun  as  a  great  rotating 
variable  magnet,  but  as  a  measure  of  the  forces  which  go  to 
make  up  the  solar  output  in  several  manifestations  of  energy. 
The  summary  of  this  line  of  thought  may  be  found  in  chap- 
ter 4  of  my  "Eclipse  Meteorology."  It  is  proper  to  renew  my 
objection  to  the  results  derived  by  other  investigators  for 
any  solar  rotation  period  which  is  shorter  than  20.68  days, 
because  it  does  not  seem  to  be  possible  in  view  of  the  above 
analysis  of  solar  conditions.  Thus,  we  must  reject  Spoerer, 
26.32;  Broun,  25.92,  25.86,  and  25.83;  Hornstein,  26.39,  26.03, 
26.24,  and  25.82;  Liznar,  26.05  and  25.96;  Muller,  25.66,  25.79, 
25.86,  25.87,  and  25.47;  von  Bezold,  25.84;  Hamberg,  25.84; 
EkholmandArrhenius,25.93;  Schuster,  25.809  or  25.825.  The 
numerous  computations,  giving  results  so  widely  different  from 
that  apparently  ruling  in  the  sun  as  derived  from  observations 
upon  its  own  material,  seem  to  indicate  that  the  application  of 
these  several  methods  of  computation  to  terrestrial  data  raises 
grave  doubts  as  to  their  value.  There  are  numerous  difficul- 
ties in  applying  least  square  methods  to  solar-terrestrial  data 
in  the  present  state  of  our  science.  The  great  fluctuations 
going  on  within  the  solar  mass  tend  to  mask  the  fundamental 
law  until  it  has  been  derived,  at  least  approximately,  by  sim- 
pler methods.  But  the  evidence  is  very  positive  that  the  equa- 
torial period  of  26.68  days  is  the  shortest  one  actually  prevailing 
in  any  portion  of  the  mass  of  the  sun. 


II.— SYNCHRONISM  OF  THE  VARIATIONS  OF  THE  SOLAR  PROMINENCES  WITH  THE  TERRESTRIAL  BAROMETRIC 

PRESSURES  AND  THE  TEMPERATURES. 


SEVERAL    OPINIONS    ON    THE    SUBJECT    OF    SYNCHRONISM. 

The  numerous  studies  during  the  past  fifty  years  into  the  ap- 
parent synchronism  between  the  solar  variations  of  energy  and 
the  terrestrial  effects,  as  shown  in  the  magnetic  field  and  the 
meteorological  elements,  have  been  on  the  whole  unsatisfactory, 
if  not  disappointing.  Just  enough  simultaneous  variation  has 
been  detected  in  the  atmospheres  of  the  sun  and  the  earth  to 
fascinate  the  attentive  student,  if  not  to  justify  a  large  expendi- 
ture of  labor,  in  view  of  the  great  practical  advantages  to  be 
obtained  in  the  future  as  the  result  of  a  complete  understand- 
ing of  this  cosmical  pulsation.  The  attack  upon  the  problem 
has  really  consisted  in  rather  blindly  groping  for  the  most 
sensitive  pulse  in  the  entire  cosmical  circulation,  and  in  disen- 
tangling the  several  interacting  types  of  impulses.  It  is  evi- 
dent that  the  partial  failures  hitherto  attending  this  work  have 
been  due  to  two  principal  causes:  (1)  The  comparison  was 
made  between  the  changes  in  the  spotted  areas  of  the  sun  and 
the  terrestrial  variations,  but  these  solar  changes  were  not 
sensitive  enough  to  register  a  complete  account  of  the  action 
of  the  solar  output.  Discussions  of  the  spots  are  being  replaced 
by  others  upon  the  solar  prominences  and  faculse,  which  respond 
much  more  exactly  to  the  working  of  the  sun's  internal  circu- 
lation. (2)  The  magnetic  and  the  meteorological  observations 
have  not  been  handled  with  sufficient  precision  to  do  justice 
to  the  terrestrial  side  of  the  comparison.  It  is  evident  that  all 
these  physical  data  at  the  sun  and  at  the  earth  must  be  com- 
puted with  an  exactness  comparable  to  that  of  astronomical  ob- 
servations of  position,  if  meteorology  is  to  be  raised  to  the 
rank  of  a  cosmical  science.  When  one  considers  the  crudeness 
of  the  meteorological  data,  taken  the  world  over,  due  to  the 
character  of  the  instruments  employed,  the  different  local 
hours  of  observation,  and  the  divergent  methods  of  reduction, 
it  is  no  wonder  that  the  small  solar  variations  have  been  swal- 
lowed up  in  the  bad  workmanship  of  meteorologists.  The 
prevailing  methods  have  been  sufficient  for  forecasting  and 
for  climatological  purposes,  but  they  are  entirely  inadequate 
for  the  cosmical  problems  whose  solution  will  form  the  basis 
of  scientific  long-range  forecasts  over  large  areas  of  the  earth, 
that  is,  for  forecasting  the  seasonal  changes  of  the  weather 
from  year  to  year.  It  is  perfectly  evident  that  if  secular  varia- 
tions of  any  kind,  such  as  the  annual  changes  in  terrestrial  pres- 
sure, temperature,  or  magnetic  field,  are  to  be  attributed  to  solar 
action,  the  original  observations  must  be  finally  reduced  to  a 
homogeneous  system.  The  local  peculiarities  of  each  station 
must  be  carefully  eliminated,  and  the  data  of  numerous  sta- 
tions must  be  concentrated  before  anything  like  quantitative 
cosmical  residuals  can  be  obtained.  When  we  consider  that 
there  have  been  numerous  changes  in  the  elevations  of  barom- 
eters, various  methods  of  reducing  the  readings,  and  many 
groups  of  selected  hours  of  observations  entering  into  the 
series  at  the  same  station,  how  could  it  be  expected  that  any 
thing  better  than  negative  results  in  solar  problems  would  be 
obtained?  The  skeptical  attitude  of  conservative  students, 
who  declare  that  the  many  indecisive  results  already  obtained 
mean  that  there  is  no  true  and  causal  solar-terrestrial  syn- 
chronism, is,  of  course,  quite  fallacious  until  it  has  been  demon- 
strated by  the  use  of  first-class  homogeneous  data  that  the 


suspected  physical  connection  is  imaginary.  There  is  but 
little  question  that  the  existing  uncertainty  is  in  fact  based 
upon  the  use  of  the  very  imperfect  methods  of  observation 
and  reduction  which  have  prevailed  in  meteorological  offices, 
rather  than  upon  the  unreality  of  the  phenomena  in  nature. 
At  present  the  difficulties  of  the  research  are  diminishing  by 
reason  of  two  improvements;  (1)  a  better  knowledge  of  where 
to  make  the  comparison,  and  ( 2)  the  gradual  acquisition  of 
reliable  secular  data.  Thus,  the  prominence  data  are  super- 
seding the  sun-spot  numbers,  and  it  has  now  become  compara- 
tively easy  to  traverse  the  magnetic  and  the  meteorological 
fields  with  our  improved  standard  curve  of  comparison,  and  to 
bring  out  the  fundamental  typical  synchronism  in  nearly  every 
series  of  observations,  so  far  as  the  annual  means  are  concerned. 

The  importance  of  emancipating  this  subject  from  the  pre- 
vailing skepticism  is  evidently  in  the  interests  of  advancing 
cosmical  science.  If  we  can  prove  that  other  forces  than  the 
Newtonian  gravitation  and  radiation  are  interacting  between 
the  sun  and  the  earth,  it  becomes  a  conclusion  of  vital  interest 
to  astronomers.  As  an  example  of  the  present  state  of  opinion, 
we  note  Prof.  Simon  Newcomb's  address"  before  the  Astro- 
nomical and  Astrophysical  Society  of  America  on  December  '29 
1902,  in  which  he  says: 

The  conclusion  is  that  spots  on  the  sun  and  magnetic  storms  are  due 
to  the  same  cause.  This  cause  can  not  be  any  change  in  the  ordinary 
radiation  of  the  sun,  because  the  best  records  of  the  temperature  show 
that,  to  whatever  variations  the  sun's  radiation  may  be  subjected,  they 
do  not  change  in  the  period  of  the  sun  spots. 

We  shall,  on  the  other  hand,  show  in  this  paper  that  ter- 
restrial temperatures  do,  as  a  whole,  change  with  the  varia- 
tions of  the  solar  prominences,  and  this  will  tend  to  modify 
Professor  Newcomb's  inference.  The  question  whether  the 
connection  is  direct  or  indirect,  by  a  magnetic  field  or  by  some 
special  action  of  radiation,  is  to  be  decided  finally  by  an  appeal 
to  the  observations.  Dr.  J.  Hann  writes  in  his  Lehrbuch  der 
Meteorologie,  pages  626,  627: 

These  can  lead  to  the  discovery  of  the  period,  but  it  is  very  difficult  to 
find  the  true  length  of  the  period,  since  the  amplitude  of  the  variation  of 
the  meteorological  elements  within  the  period  is  not  very  great,  because 
so  many  other  influences  are  present,  which  stand  in  the  way  of  deriving 
more  accurate  mean  values  out  of  long  intervals  of  time.  As  yet  no  one 
has  succeeded  in  surely  deducing  for  any  one  meteorological  element  a 
cyclic  variation  of  considerable  amplitude. 

These  efforts  have  been  applied  to  variations  of  tempera- 
ture, clouds,  rainfall,  thunderstorms,  hail,  barometric  pres- 
sures, cyclones,  and  winds,  especially  with  the  view  of  finding 
an  11-year  period  synchronous  with  that  of  the  sun  spots.  It 
should  be  noted  that  a  shorter  period,  of  about  three  years,  is 
probably  the  better  period  of  synchronism  to  be  studied.  Also, 
synchronous  movements  need  not  be  truly  periodic.  Indeed, 
there  may  be  true  correspondence  with  very  irregular  and 
aperiodic  changes.  It  is  easier  to  connect  loosely  constructed 
variations  in  the  prominences  of  about  three  or  four  years 
duration  with  terrestrial  variations  than  to  establish  synchro- 
nism in  the  11-year  sun-spot  period.  Dr.  A.  Sprung,  in  his 
Lehrbuch  der  Meteorologie,  pages  366,  367,  writes: 

Therefore,  a  connection  between  the  sun-spot  frequency  and  the  changes 
in  our  atmosphere  can  not  well  be  denied.  It  is  probable  that  the  pe- 

17  Science,  January  23,  1903. 


10 


riodic  changes  in  the  atmosphere  are  not  caused  directly  through  the 
sun  spots,  but  that  both  phenomena  are  brought  about  through  one 
common  or  by  several  interacting  causes,  whereby  a  displacement  of  the 
periods  relative  to  one  another  becomes  possible. 

Prof.  Cleveland  Abbe  has  frequently  expressed  in  the 
MONTHLY  WEATHER  REVIEW  a  very  doubtful  view  regarding  the 
advisability  of  such  researches,  with  the  object  of  discouraging 
further  efforts  to  unravel  the  solar-terrestrial  net.  Thus,  in 
the  MONTHLY  WEATHER  REVIEW  for  June,  1901,  page  264,  he 
writes: 

As  the  periodicities  in  sun  spots,  the  width  of  the  spectrum  linos,  the 
magnetic  and  auroral  phenomena  are  sufficiently  well  marked  to  be  satis- 
factorily demonstrable,  while  corresponding  variations  in  pressure,  tem- 
perature, wind,  and  rainfall  are  small,  elusive,  and  debatable,  we  must 
caution  our  readers  against  being  carried  away  by  optimistic  promises. 
It  is  certainly  impressive  to  the  thoughtful  mind  to  realize  that  there  is 
even  a  slight  connection  between  solar  and  terrestrial  phenomena,  but 
the  delicacy  of  this  connection  is  such  that  it  still  remains  true  that  the 
study  of  meteorology  is  essentially  the  study  of  the  earth's  atmosphere 
as  acted  upon  by  a  constant  source  of  heat  from  the  sun.  None  of  these 
astrophysical  studies  should  tempt  the  meteorologist  to  wander  far  from 
the  study  of  the  dynamics  of  the  earth's  atmosphere  and  the  effects  of 
the  oceans  and  continents  that  diversify  the  earth's  surface. 


f.OO 
f.ZO 


"•60 


3.40 
9.  fq 
3.0O 
8.80 


(2SJ 


(10)       ^ 


of 


200 
ISO 

too 


Cu 


of  J90? 


FIG.  5.— Solar  and  terrestrial  synchronism. 

We  have,  nevertheless,  merely  to  recall  the  works  of  many 
scientists  in  order  to  realize  how  strong  a  hold  this  problem 
has  upon  the  astrophysical  meteorologist:  Herschel,  1800; 
Gautier,  1844;  Fritsch,  1854;  Arago,  1855;  Zimmermann, 
1856;  Wolf,  1859;  Meldrum,  1870;  Koeppen,  1873;  Hill,  1880; 
van  Bebber,  1882;  Blanford,  1889;  Bruckner,  1890;  Lockyer, 


1898;  Carrington,  Spoerer,  Wolfer,  and  many  others.  The 
number  of  students  who  are  taking  up  the  problems  of  cos- 
mical  meteorology  is  rapidly  increasing,  and  this  shows  that 
there  is  encouragement  for  such  work. 

The  present  paper  continues  the  discussion  of  an  investi- 
gation first  published  in  1894,18  which  brought  out  the  fact  that 
there  is  a  synchronous  variation  in  short  cycles  of  about  three 
years  duration  superposed  upon  the  11-year  sun-spot  period. 
In  Bulletin  No.  21,  Solar  and  Terrestrial  Magnetism,  page 
127,  it  was  said: 

A  comparison  of  the  mean  American  meteorological  curve  with  tho 
European  magnetic  curve  certainly  shows  conformity  to  such  an  extent 
as  to  exclude  merely  accidental  physical  relations.  Should  such  a  result 
be  obtained  also  in  the  future,  it  will  bo  a  demonstration  of  the  synchro- 
nism of  tho  two  systems  of  forces  under  consideration. 


JS72        J87S              JS90               J83S               1O9O               J895             l&OO 

2OO 

100 

0 

T 

\ 

jT\ 

r-     / 

\X^\ 

/      ^ 

\ 

•^ 

fV/ 

V 

/ 

^. 

^^-^.y 

\. 

Pffjmincr 

ices  on  th 

e  Sun. 

"^  ^ 

+20 

o 

-20 

•HO 
O 
-10 

+10 
0 
-10 

+10 
0 
-10 

+20 

o 

-20 

+10 
0 
-10 

+20 

o 

-20 

+20 

0 

-20 

+20 
O 
-20 

+3O 
O 
-30 

/\ 

M 

A       / 

^       /   \ 

f\ 

~^\ 

/    \ 

\     / 

V7     V 

>    \ 

•-  -^^ 

\ 

\ 

"  —  •*' 

,  \  s 

"N 

V. 

/       \J 

,VfH'  A/ft 

'A  Wales.  ( 

$1  \/ 

/\ 

(\ 

s~\        f 

/   \ 

f\          ^ 

/   \ 

\    / 

\  I 

~        W 

\  / 

"^—^       V 

L      \  S 

^JjVor 

"tk  India.  (3j 

X-V 

/- 

•^ 

/\ 

-->       / 

\  /\ 

/  \ 

^-^ 

/          ^ 

\-S 

V 

/        Vx 

\J 

Centn 

*l  India.  (4J 

\s 

A 

/ 

17 

\      /\ 

A 

7  \ 

n      t 

\    /    \H 

/I 

^    1 

J    \  J 

V-x- 

,  v  ; 

\  } 

\^r 

Soub 

^.  India,  (51 

f~\ 

x  —  s.        J 

V                    -, 

A. 

/\ 

Z—^. 

\  y\ 

_              ^  V 

A 

-S~ 

U        \ 

/ 

X 

\- 

'      JVort 

h  China.  (3) 

Qk 

r\ 

r\ 

x^~ 

-  s\ 

^  ^~S 

\ 

A  /  V 

/  \ 

o 

\     f\ 

/  2    v 

/    V^ 

Ja 

naj?,.  f-^A 

} 

-\ 

/•^ 

V^      / 

—  N     / 

"~—\ 

•^\^s 

\J_ 

\S  \. 

;C\  / 

Coast  Cape  Co  font/  J  4  r* 

v 

y-v 

"-—  -^ 

/\  ^ 

/  v/\ 

^^         ^_^ 

~  / 

\^s 

Inland  G. 

'woe  ColonirJ37*-^ 

Plateau.  Cave  Colonu.(2) 

^^r\ 

^ 

/~—~^       j 

\ 

^     , 

\y 

\  »* 

\ 

x  ' 

^~"^ 

i  V 

r\ 

*  f\ 

\ 

A 

/   \ 

\ 

/  \ 

1     \        / 

\ 

/ 

\  ,  ^ 

\           , 

\  /   \ 

\       I 

\       / 

,  / 

v/ 

\       / 

^    I 

/        \ 

\I 

s  / 

\    J 

1 

/A 

\J 

/<  '('/(ffir/.  '(Jrf<t*si?-a\ 

&.(<S)  \j 

1 

FIG.  6. — Variations  of  the  annual  pressure  in  the  direct  type. 

18  Inversion  of  Temperature  in  the  26.68-day  Solar  Magnetic  Period. 
Amer.  Journal  of  Science.    Vol.  XLVIII.     December,  1894. 


11 


Since  that  time  advances  have  been  made  as  follows: 
The  magnetic  curve  has  been  extended  from  1841  to  1900; 
the  barometric  pressures  of  the  United  States  have  been  re- 
duced to  a  homogeneous  system;  the  curves  of  prominence 
frequency  on  the  sun  have  been  computed  by  Lockyer  and  in- 
dependently by  myself;  the  variations  of  the  prominences  have 
been  closely  associated  with  the  changes  in  the  angular  veloc- 
ity of  the  solar  surface  rotations  in  different  zones,  especially 
in  the  polar  latitudes;  the  type  of  internal  circulation  neces- 
sary to  produce  this  polar  retardation,  and  to  transform  the 
solar  mass  into  a  polarized  magnetic  sphere,  has  been  indicated 


of  the  earth.  These  have  a  variation  in  direct  synchronism 
with  the  prominences,  in  certain  parts  of  the  earth,  but  under 
special  conditions  of  orography  the  synchronism  is  of  the  in- 
verse type.  This  chain  of  evidence  is  strong  enough  to  induce 
confidence  in  regard  to  the  fact  that  this  solar-terrestrial  phys- 
ical synchronism  really  exists. 

THE    UNSATISFACTORY    STATE    OF    THE    OBSERVATIONAL    DATA. 

The  two  prevailing  difficulties  in  extracting  suitable  data 
from  the  published  reports  of  meteorological  observatories, 
and  reducing  them  to  a  homogeneous  system,  are  the  numer- 
ous changes  in  the  elevation  of  the  barometers,  and  in  the 
very  different  hours  of  making  the  observations.  Without  the 
expenditure  of  labor  entirely  beyond  the  capacity  of  a  single 
office  to  bestow  upon  the  task,  when  the  research  for  synchro- 
nism is  extended  to  the  entire  earth,  it  has  been  necessary  to 


1872     1375 

138O              18&5 

/<$<w             /sftf           y^a? 

SOO 
100 
O 

Z_ 

\ 

/^^ 

^ 

Z5 

/   \> 

^ 

^ 

/  v/ 

\ 

/ 

v^^ 

x^          J 

V 

/ 

N^ 

—*^ 

Promine* 

tcqs  on  the  i^fifn 

*Ss 

+2O 
0 
-20 

+  20 
O 
—20 

+20 
O 
-2O 

+30 
O 
-30 

+30 
0 
-30 

+SO 
O 
20 

France. 

^ 

/~\ 

/~\ 

A 

/  \s  — 

/ 

2 

\  / 

Llx^ 

^    f\ 

/ 

ft    1 

1  /   \ 

V  / 

s  z 

H   V 

/ 

s 



/  \ 

Spain. 

r\ 

/  ^ 

r 

\       f 

1  /    \ 

/ 

A      A 

\ 

/ 

/ 

Nl7 

u    \ 

7  V 

Q  / 

_E 

.^  '  — 

Vy 

) 

\  f\f\ 

A    /A 

/  —  X 

/ 

f\    j 

\  A 

f  \ 

V  /" 

,      / 

>  —  / 

™ 

w 

/         \ 

^—/ 

&au.ffa 

wz  £  uro  oe.     V 

/ 

/r>v 

J. 

'X— 

2S 

s 

/  _ 

. 

s^~\ 

O 

x^       \ 

/ 

N^          , 

_    \ 

1 

P 

1 

/ 

\  z. 

\ 

/  1 

j       JVor 

gg 

Russ 

/a;.    ^^ 

\  

/ 

r\ 

/ 

rJ\ 

A 

^y^ 

/\ 

— 

5 

' 

^  » 

i    ) 

v  • 

\ 

v 

w 

2E 

-t  J 

t. 

1  — 

/~\ 

'•N 

/ 

^^^   ~\ 

^~ 

\    / 

VA 

~^°\  

\. 

^- 

vX  ' 

Pf  \ 

+30 

o 

-30 

33 

Russi 

cz 

_^ 

\ 

-. 

\ 

^^^ 

Q 

/\   / 

\   /A  / 

^_/ 

\ 

^y  \ 

/         \y 

\y  w^     — 

^  i*V?  ff*(7^  iSf&(*2*CCK 

FIG.  1. — Variations  of  the  annual  pressure  in  the  inverse  type. 
In  the  present  paper  we  shall  show  the  results  of  a  discussion 
of  the  annual  residuals  of  pressure  and  temperature  in  all  parts 


FIG.  8. — Variations  of  the  annual  pressure  in  the  indifferent  type. 

use  some  simple  devices  for  the  sake  of  arriving  at  approxi- 
mately homogeneous  residuals.  The  work  for  the  United  States 
is  complete  for  the  pressures,  and  is  in  progress  for  the  tem- 
peratures. By  inspecting  my  Barometry  Report19  it  is  easy  to 
see  the  reason  for  the  necessity  of  the  reduction.  In  order  to 
give  some  idea  of  the  state  of  the  data  in  other  countries,  we 
note  the  following  with  respect  to  the  barometric  pressures: 

For  Russia-Siberia,  several  stations  changed  elevation  more 
than  once. 

India,  there  are  numerous  changes  of  elevation. 

South  Africa,  numerous  changes  of  elevation,  and  also  of 
the  hours  of  observation. 

New  South  Wales,  the  monthly  means  of  observations  alone 

19  Eeport  of  the  Chief  of  the  Weather  Bureau,  1900-1901,  Vol.  II. 


12 


ta-rr    rsrs          2880          laas          1090            lays          ixo 

/ 

X\ 

200 

/ 

_5«^5_\ 

/        ^^ 

c 

^   \^x 

\ 

/ 

^-^ 

100 

"V^          i 

V 

Promint 

>nces  on 

/ie  Sim. 

^^•^ 

o 

t. 

x-^ 

t-J.O 

/•  —  N 

r-   ^ 

"\     /     \ 

*  ** 

^—^ 

o 

.»  

_     \ 

7  v^ 

v  ^  —  r' 

—UO 

v— 

^Wew  iSoittA  Wa6es.  (JOI 

+1.0 

r\  . 

/     ^ 

.  

o 

>v_ 

v/    ^^  — 

—l.O 

/SotitA^ 

4_ustml(a 

•(<?) 

/\ 

+1.O 

/   v_ 

^y\ 

^.— 

/-\ 

o 

-w 

0 
-1.0 

+IJD 

0 

-uo 

+J.O 

o 

^  *" 

' 

We&t 

4u&trvdi 

a.  (<9/ 

y  \ 

/—^ 

,  —  v 

/~\.       / 

^-v.. 

\^  

•  —  —  /       ^ 

"*"    ^  x 

>  —  ' 

J3a.ta.vi 

z  and  lA^otniilcc.  . 

25 

^_^ 

^       ^^ 

S~*\^  ^ 

""*'  — 

-•     V. 

- 

^fncfcfjyof^i 

a     /4) 

^^ 

_^-^ 

^^^ 

/r\/ 

/  ^**-S 

—  ' 

/ 

+1.0 

o 

«/i 

€aur"tttiu 

-.13) 

y~\ 

^^^^ 

^^ 

^x  —  v^ 

"*•  —  ^" 

^^      "N 

—  ~^^_X^ 

—1.0 
+1.0 

o 
-W 

+1.0 

o 

Cei/iojz.(6i 

_-x*  —  V 

_    \^ 

\_x 

\ 

-/  1\/ 

In 

•2ia,—JJow 

/W^  v 

_^.  —  «. 

JU 

adagasci 

r>.(2)  — 

—W 
+1.0 

o 

-1.0 

+J.O 
0 

-1. 

^-*^ 

a 

ntralAl 

ricccJ6t~ 

/  \  / 

\            / 

/"\ 

V  /          "*• 

West  Africa. 

(S) 

M72        1875                J880                23SS                289O                 1895               1$OQ 

f 

\ 

/^V 

r-     1 

^^\ 

/  s 

^^ 

^^ 

f\J 

Y 

/ 

wo 

N—  ^  J 

^V 

Prominences  art  the  £>u.n. 

>s-  *. 

F° 

+!.0 
0 
-7.0 

+1.0 
0 

South  Africa. 

.(20) 

^/~\y 

"X     j^^~\ 

y^^^      -^ 

^^    \ 

/  ^~~^ 

South 

Americ 

*,.(J5) 

/\       XN 

~->k 

f\ 

y^v  ^-v 

zs 

/ 

\    / 

Vx 

U    \S- 

\ 

X      ^~ 

X   / 

+1.0 
0 
-1.0 

+1.0 
0 
-1.0 

+1.0 
0 
-1.0 

+w 

0 
-1.0 

+1.0 
0 
-1JO 

+1.0 
0 
-1.0 

V.o 

0 
—1.0 

+1.0 

o 

rvx-s 

Santia. 

5>»   «^9  CAilt. 

/ 

^\ 

Q    /" 

/~^*^, 

\^r-*^ 

*/         \J 

\s 

West  Indies. 

<•  —  ^ 

r~  ^**—sr 

^Azores 

crnd  Jtfadeirvt,  .  13) 

"11 

—  ^  x\ 

^X     ^^" 

"  \^^ 

^X^ 

,^v 

S\  North  Africa 

(J2)      x 

2—  2 

V 

y^ 

Vz 

\ 

/ 

'  

s~ 

\^s  

\ 

z 

\_ 

X 

,-N  South  West  En 

rvp>e.(12i 

^  x- 

.^•^^.^ 

<\ 

x  —  v 

r\  r 

/ 

~  

v»> 

\^~- 

\  , 

-s\f 

w 

\y 

r^ 

VestJ5ur>t 

7ve.  rf$) 

/^N 

_x^"~X 

\j^J^ 

r    /  \ 

/ 

\        , 

"x  /n^^ 

w 

~    1        i 

^. 

West 

Given  land.  i~i4)  i 

\ 

/\ 

( 

\      r\ 

/    \ 

—  -  \ 

r\ 

I       P 

/ 

/ 

f 

* 

\  r\ 

V     / 

J 

f\      I 

2-4 

\J 

LJ 

\AJ 

\. 

\y 

y-*v 

S~  "*• 

23 

-4 

\  £s 

•  —  «- 

X\        r 

™ 

r 

^^J 

\x 

+1.0 
0 
-1.0 

_     Pacific  States 

.(fO) 

^^ 

<—  ^         ^  s. 

,^-s. 

•^      \-x 

v-v_ 

'ffonolirfu 

FIG.  9.— Variations  of  the  annual  temperature  in  the  direct  type. 


were  published.  These  had  to  be  collected  before  the  annual 
means  could  be  computed. 

Argentina,  the  monthly  means  of  observations  alone  were  pub- 
lished, and  these  also  had  to  be  collected  before  the  annual  means 
could  be  computed.  The  stations  have  quite  short  records. 

Iceland  and  Greenland,  very  few  changes  in  elevation,  but 
not  long  records. 

In  general  all  the  annual  pressure  curves  were  plotted,  and 
a  mean  pressure  and  normal  gradient  were  determined,  from 
which  the  amplitude  variations  were  taken  off  as  residuals. 
Since  our  purpose  was  simply  to  secure  the  most  probable 
annual  residuals  this  graphic  method  was  substituted  for  the 
exact  computations  which  ought  to  be  made.  Frequently  the 
secular  gradient  slope  was  so  prominent  throughout  the  series 


for  a  single  station  as  to  suggest  a  gradual  change  in  the  cor- 
rection of  the  barometer  relative  to  a  normal  standard. 

With  respect  to  the  temperatures,  the  annual  means  were 
extracted  from  the  reports,  and  the  mean  values  for  the  several 
series  were  computed,  so  far  as  they  were  apparently  homo- 
geneous, and  from  these  the  residuals  were  formed.  As  the 
cosmical  annual  variation  of  temperature  is  only  1°  to  2°  F., 
it  was  often  possible  to  break  up  a  long  series  at  the  same 
station  into  homogeneous  sections;  but  this  was  done  cau- 
tiously, and  only  after  clear  evidence  of  a  discontinuity  in  the 
local  conditions.  The  great  difficulty  with  the  temperature 
data  consists  in  the  numerous  hours  of  observation  that  have 
been  adopted,  or  in  the  numerous  selected  groups  of  hours 
from  which  the  means  were  derived.  Many  of  these  differ- 


13 


ences  arose  from  artificial  attempts  to  obtain  an  approximately 
correct  24-hour  mean,  to  which  in  fact  all  meteorological  data 
should  be  very  carefully  reduced.  Some  of  the  combinations 
of  hours  used  are  as  follows: 

United  States,  Washington  mean  time,  7:35,  4:35,  11:35; 
7:35,  4:35,  11:00;  7,  3,  11.  Seventy-fifth  meridian  time,  7,  3, 
11;  7,  3,  10;  8,  8;  maximum,  minimum. 


1872       1S75              1880              1685               189O               1895              19OO 

200 
100 
0 

z_ 

\ 

^\ 

/ 

^zrs 

/       V" 

\ 

x 

C\J 

\ 

/ 

V  x 

\  y 

v 

s 

^V 

"    ' 

^^  _ 

Prominences  on  ii 

re  Sun. 

F.° 

-l.o 
o 

-1-1.0 

-1.0 
0 
+1.0 

-1.0 

o 

+  10 
-1.0 

o 

+1.0 

—1.0 
0 
+1.0 

-1.0 

o 

+1.0 
-1.0 

o 

+1.O 
-1.0 

o 

+1.0 
—l.O 

o 

+1.0 

-2.0 
0 
+1.0 

-1.0 

o 

+10 

75 

JaDOJi.llSI 

^^ 

~    / 

c  A 

£\ 

^  s^ 

'    \_^ 

—  \ 

Z_AJ 

^—/ 

\ 

/ 

-*— 

132552! 

tna.J2) 

s~*\ 

_      / 

\       /-^ 

Z-JuZ 

\-~. 

v       / 

2    V^ 

/•    v^ 

-5^7  \ 

y    Q 

V— 

"""—  ^ 

SJl.  Chin 

i3S 

Z_j 

A, 

2_S 

\  ^_ 

^/     ^ 

~^^^_^ 

S.W.  Russia..  I  191 

' 

\              y 

^ 

/-\ 

,^\ 

1 

V          / 

\     ^ 

/    V 

-  /  \ 

A    r- 

/ 

\      / 

\J   ^ 

_  y 

\/    3 

'    vy  ^«_ 

z  / 

L                \        / 

' 

\ 

\ 

...  Centr 

^  Russia.  I  101 

S    r 

\       /"*- 

-  A 

Q 

'  V 

\  f 

E2_ 

\J  \ 

/"  — 

V-  v    / 

\     \J 

^^ 

\X              V 

/ 

\ 

3 

/> 

s 

A 

i 

/  \ 

\    r- 

\ 

/ 

r~ 

/  ^ 

\  / 

/" 

\  j  V 

/       / 

v  / 

\J 

vx 

^   \ 

/.    V/ 

vy 

,yK  W.Ru^ta.:t.9l 

A 

f. 



/ 

v    /  V 

\  - 

/    v- 

"--*—  "^^^        / 

—\ 

/ 

*"v-J      V 

'  \y  v/ 

•HI^^^ 

\/^ 

/ 

Centr 

«(T  Enron 

e.(17) 

\> 

(\ 

A 

\ 

\ 

/   \ 

zs 

3     / 

\ 

/     \ 

\ 

j      y 

\ 

/       \     ' 

-•  —  •" 

N. 

'     v_y 

U 

x     V/ 

Faroe  /s-< 

and&i  let 

iia.nct.-  E.  GreenLa 

rut.  (4-) 

x  / 

^             1 

vy 

s 

J 

v_        /-\  / 

\ 

\|y    V 

v  /-\ 

Souths 

ltlcmtic"States  .  1 

g 

/ 

-\ 

\  y 

^ 

\r\ 

^  / 

\          "i 

vy 

\  / 

A   / 

^_  V 

\  y  v 

Wfe5-£l    <£/< 

if  State  S./J7J 

/ 

\ 

A/ 

^/^ 

XN 

\ 

/ 

:  i 

Z-  1  - 

\s 

\     0 

j 

v. 

^,           / 

\^     /-v 

\  / 

£ak 

?Recrion  111)  \J 

v'\y^ 

v  ; 

FIG.  10. — Variations  of  the  annual  temperature  in  the  inverse  type. 

New  South  Wales,  9  a.  m. ;  9,  3,  9;  maximum,  minimum. 
South  Australia,  9,  3,  9;  9,  12,  3,  6,  9;  maximum,  minimum. 
West  Australia,  9,  3;  9,  12,  3;  9  a.  m. ;  6,  6;  maximum,  mini- 
mum. 

Ocean  Islands,  hourly;  9,  3,  9,  minimum;  6,  9,  1,  3,  3:58. 


Japan,  9:30,  3:30,  9:30;  4-hourly,  or  2,  G,  10,  2,  6,  10. 

China,  hourly;  10,  4,  10. 

India,  8,  10,  4;  10,  4;  6-hourly,  or  10,  4,  10,  4;  9:30,  3:30; 
9,  4;  10:30,  3:30;  maximum,  minimum. 

Russia-Siberia,  7,  1,  9;  7,  2,  9;  9,  12,  9;  8, 1,  9;  hourly. 

Europe,  7,  2,  9,  9;  7:45,  8;  6,  2,  10;  3-hourly;  maximum, 
minimum;  7,  10,  1;  4,  7,  11;  7,  1,  7;  6,  9,  12;  3,  6,  9;  6,  12,  9; 
hourly. 

Azores-Madeira,  9,  3,  9. 

North  Africa,  7,  2,  9;  7,  11,  2,  5;  7, 1,  6;  9,  3,  9. 

South  Africa,  6,  12,  6;  6,  2;  9,  9;  8,  8;  8  a.  m. 

South  America,  7,  2,  9;  hourly. 

Iceland-Greenland,  8,  2,  9. 

From  such  an  exhibit  it  is  no  wonder  that  meteorology  has 
not  yet  contributed  its  proper  share  to  accurate  cosmical  phys- 
ics. It  is  needless  to  recount  the  reason  for  this  state  of  affairs, 
but  only  to  urge  as  speedy  a  remedy  as  is  possible.  It  might 
be  argued  that  no  results  can  be  derived  from  such  data;  but 
this  is  not  true,  as  a  study  of  the  residuals  summarized  in  this 
paper  amply  confirms.  It  is,  perhaps,  surprising  that  valuable 
results  can  be  extracted  from  the  data,  and  this  only  proves 
how  important  such  work  might  be  made  if  sufficient  care 
were  exercised  in  selecting  the  hours  of  observation,  and  estab- 
lishing rigorous  methods  of  reduction.  It  frequently  happens 
that  at  a  given  station  the  same  hours  continue  to  be  used  for 
many  years,  so  that  in  effect  its  own  residuals  are  nearly  homo- 
geneous. The  means  of  the  various  combinations  of  selected 
hours  generally  approximate  a  true  24-hour  mean,  so  that  on 
the  whole  there  is  something  like  homogeneity  in  the  differ- 


1900 


200 

10O 

O 


+1.0 

o 

—l.o 


+1.0 

o 

-1.O 


+1.0 

o 

-1.0 


+1.0 

o 

-1.0 


•aa 

o 
-w 


+1.0 

o 

-w 


^7 


3 


Prominences  on 


India-  Elera,ted,. 


^ 


\f 


£ 


/v- 


Central.  jSlberila. . 


X? 


S 


£ 


ituitic  StettessJ 


y_s 


A 


j- 


ttafcs.fM 


A^ 


Fia.  11. — Variations  of  the  annual  temperature  in  the  indifferent  type. 

ent  changes.  The  fact  that  residuals  synchronous  with  solar 
variations  actually  survive,  is  a  satisfactory  evidence  that  the 
causes  producing  them  are  solar  and  not  local  terrestrial. 

It  is  not  possible  to  print  in  the  MONTHLY  WEATHER  REVIEW 
the  table  of  residuals  for  each  station,  and  we  must  confine 


14 


FIG.  12. — Distribution  of  the  pressure  types. 


Fia.  13. — Distribution  of  the  temperature  types. 


ourselves  to  the  curves  representing  the  mean  residuals  for  a 
group  of  stations,  the  number  being  entered  in  connection 
with  the  name  of  the  country.  Thus,  for  New  South  Wales 
the  pressure  curve,  fig.  6,  was  determined  from  six  stations, 
Albany,  Bathurst,  Deniliquin,  Goulborn,  Newcastle,  Sydney. 


RESULTS    OF    THE    OBSERVATIONS. 


The  argument  for  solar  and  terrestrial  synchronism  may  be 
recapitulated  as  follows: 

Bigelow's  curves  for  1894  showed  a  synchronism  in  a  short 
period  of  about  three  years,  superposed  upon  the  11-year  sun- 
spot  curve,  for  the  following  elements:  Terrestrial  magnetic 


field,  American  temperatures,  pressures,  storm  tracks  in  longi- 
tude and  latitude,  and  cold  waves  in  latitude.  In  1902  Lock- 
yer  worked  out  the  annual  variation  in  the  solar  prominences 
and  arrived  at  the  same  system  of  minor  crests  in  the  sun  that 
had  previously  been  determined  at  the  earth.  These  curves 
are  shown  on  fig.  5,  "  Solar  and  terrestrial  synchronism." 

A  study  of  the  temperature  and  the  pressure  residuals  for 
the  entire  earth  shows  that  the  phenomena  of  inversion  pre- 
vails in  the  earth's  atmosphere,  localizing  the  effect  of  solar 
action  in  two  typical  curves  which  are  the  inverse  of  one 
another.  I  have  previously  found  a  form  of  inversion  of  en- 
ergy in  the  terrestrial  magnetic  field,  and  efforts  have  been 


15 


made  to  explain  the  phenomenon.  Besides  the  secular  inver- 
sion here  illustrated,  I  have  found  a  semiannual  inversion  in 
the  meteorological  elements  of  the  United  States,  as  stated  in 
other  places,  and  much  work  has  been  done  in  developing  this 
important  fact. 

We  have  treated  the  secular  inversion  as  follows:  The  curves 
of  the  mean  residuals  of  the  pressures  and  temperatures,  taken 
by  geographical  groups  as  indicated,  were  plotted  to  scale  and 
compared  with  the  Lockyer  solar  prominence  curve  as  to  the 
recurrence  of  the  successive  maxima  and  minima.  They  were 
then  associated  in  three  groups,  as  follows: 

I.  Direct  type,  wherein  the  solar  and  the  terrestrial  maxima 
closely  match  each  other  throughout  the  interval  1873-1900. 

II.  Inverse  type,  wherein   the   terrestrial  curves  must  be 
inverted  to  make  the  maxima  coincide. 

III.  Indifferent  type,  wherein  there  is  not  sufficient  evidence 
of  conformity  with  the  type  curve  to  be  satisfactory. 

There  may  be  differences  of  opinion  as  to  the  assignment  of 
some  of  these  curves,  but  the  reader  can  make  any  different 
arrangement  that  he  prefers.  It  seems  to  me  that  the  general 
fact  of  synchronism  is  so  pronounced  as  to  call  for  the  careful 
consideration  of  meteorologists.  Fig.  6,  "  Variations  of  the  an- 
nual pressure  in  the  direct  type; "  fig.  7,  in  the  " inverse  type; " 
fig.  8,  "indifferent  type; "  fig.  9,  "Variations  of  the  annual  tem- 
perature in  the  direct  type; "  fig.  10,  in  the  "inverse  type;  "  and 
fig.  11,  in  the  "indifferent  type,"  are  sufficiently  explicit  with- 
out further  explanation.  The  unit  for  the  pressure  variation  is 
0.001  inch,  and  that  for  the  temperature  is  1.0°  F.  The  average 
range  in  annual  pressure  amplitude  amounts  to  as  much  as  0. 060 
inch  and  that  for  the  temperature  to  2°  or  3°  F,  more  or  less. 

DISCUSSION    OF    THE    LOCAL    INVERSIONS. 

These  suggestive  curves  deserve  more  discussion  than  is 
possible  in  this  connection,  but  fuller  data  and  further  re- 
marks will  be  found  in  a  forthcoming  report,  which  will  con- 
tain the  original  data  in  full.  It  may  be  desirable  to  call 
attention  to  the  geographical  distribution  of  the  types  of  syn- 
chronism thus  indicated,  by  plotting  on  world  charts  D,  I,  and 
#,  respectively,  for  the  direct,  inverse,  and  indifferent  types. 
Fig.  12,  "  Distribution  of  the  pressure  types,"  shows  that,  taking 
the  earth  broadly,  the  region  around  the  Indian  Ocean  gives 
direct  synchronism,  South  America  and  North  America  give 
inverse  synchronism,  while  Europe  and  Siberia  give  an  indif- 
ferent type.  Greenland  and  Iceland  seem  to  have  direct  type 
like  the  Indian  Ocean.  Fig.  13,  "  Distribution  of  the  tempera- 
ture types,"  shows  that  there  is  synchronism  of  the  direct  type 
for  the  Indian  Ocean,  Africa,  South  America,  the  West  Indies, 
and  the  Pacific  islands  generally — that  is  to  say,  throughout 
the  Tropical  Zone.  The  inverse  or  the  indifferent  types  pre- 
vail in  Asia,  Europe,  and  North  America  generally — that  is, 
throughout  the  North  Temperate  Zone. 

Taking  the  earth  as  a  whole,  the  temperatures  synchronize  di- 
rectly with  the  solar  energy  in  the  Tropical  Zone,  and  inversely 
in  the  temperate  zones.  The  indifferent  type  prevails  in  the 
plateau  districts  of  the  continental  areas,  probably  because  the 
solar  type  is  there  so  broken  up  by  the  local  climatic  conditions 
as  to  practically  obscure  the  synchronism.  In  the  pressures  the 
Eastern  Hemisphere  tends  to  direct  synchronism,  except  in 
Europe  and  Russia,  where  the  indifferent  type  prevails,  and 


the  Western  Hemisphere  to  the  inverse  type.  It  may  not  be 
practicable  to  explain  all  that  this  means,  but  apparently  we 
are  dealing  with  the  complication  caused  by  superposing  an 
atmosphere  in  circulation  upon  the  unequally  heated  surface  of 
the  earth.  The  surging  of  the  atmosphere  as  a  whole  from  one 
hemisphere  to  the  other,  or  from  the  continents  to  the  oceans,  is 
concerned  in  producing  these  effects.  The  trend  of  the  great 
mountain  systems  strongly  differentiates  the  circulation  of  the 
lower  strata.  Thus,  the  Himalaya  Mountains,  running  east  and 
west,  check  the  flow  of  air  from  the  Tropics  to  the  Asiatic  Con- 
tinent, while  the  Rocky  Mountains  and  the  Andes  system  favor 
the  flow  along  the  meridians,  especially  in  the  United  States. 
As  a  result,  the  number  of  cyclones  crossing  the  United  States  is 
many  times  the  number  crossing  Siberia,  which  is  in  fact  singu- 
larly deficient  in  cyclones.  South  America  shows  a  similar  de- 
fect in  circulation,  because  it  lies  too  near  the  Tropical  Zone. 

The  United  States  is  covered  by  an  active  circulation  be- 
tween the  Tropics  and  the  north  Polar  regions,  Siberia  by  a  stag- 
iinnt  atmosphere,  and  Europe  generally  by  a  mixed  and  in- 
different circulation,  since  the  American  cyclones  tend  to  break 
up  upon  the  territory  of  Europe  after  crossing  the  Atlantic 
Ocean.  Hence,  the  region  about  the  Indian  Ocean  is  favor- 
able for  detecting  direct  synchronisms  of  pressure  and  tem- 
perature with  the  solar  prominences  by  reason  of  its  quiescent 
atmosphere,  and  the  United  States  is  well  placed  to  respond 
to  an  inverse  synchronism,  by  reason  of  its  active  circulation 
with  a  pronounced  component  from  the  north  Polar  regions. 
Europe  does  not  possess  an  atmosphere  which  registers  the  so- 
lar and  terrestial  synchronism  in  a  very  efficient  manner.  This 
may  account  for  the  fact  that  the  European  attempts  to  establish 
a  definite  synchronism  have  issued  generally  with  negative 
results.  As  has  already  been  suggested,  too  much  emphasis 
has  been  put  upon  the  failures  to  make  out  the  connection 
between  the  solar  and  the  terrestrial  synchronisms. 

It  should  be  noted  that  C.  Nordmann20  and  A.  Angot21  de- 
duced for  certain  tropical  stations  small  residuals  of  tempera- 
ture which  are  inverse  to  the  sun-spot  curve,  but  apparently 
synchronous.  These  authors  have  smoothed  their  curves  by 
grouping  successive  years,  and  have  reached  small  residuals. 
Since  synchronism  should  display  the  annual  variations  intact, 
as  given  above,  it  may  be  questioned  whether  any  process  for 
eliminating  the  minor  deflections  from  year  to  year  is  desirable. 

We  also  note  the  important  fact  that  the  wide  amplitudes 
which  are  characteristic  of  the  11-year  sun-spot  curve,  and 
which  it  has  been  chiefly  sought  to  discover  in  the  meteoro- 
logical elements,  does  not,  according  to  this  research,  appear 
at  all  prominently  in  the  residuals.  It  is  only  the  short  period 
of  about  three  years  that  displays  the  solar  terrestrial  syn- 
chronism. I  am  not,  at  present,  able  to  indicate  what  this  re- 
sult implies  in  solar  physics,  but  it  certainly  carries  with  it  a 
change  in  our  method  of  approaching  the  entire  problem. 

20  The  periodicity  of  sun  spots  and  the  variations  of  the  mean  annual 
temperatures  of  the  atmosphere.     M.   Charles  Nordmann.     Comptes 
Eendus.     Paris,  June,  1903.     Translation  in  Monthly  Weather  Review, 
August,  1903.     P.  371. 

21  The  simultaneous  variations  of  sun  spots  and  of  terrestrial  atmos- 
pheric temperatures.     Prof.  Alfred  Angot.     Annuaire  de  la  Soci6te  Me- 
teorologique  de  France,  June,  1903.     Translation  in  Monthly  Weather 
Eeview,  August,  1903.     P.  371. 


III.— THE  PROBLEM  OF  THE  GENERAL  CIRCULATION  OF  THE  ATMOSPHERE  OF  THE  EARTH. 


THE    CANAL    THEORY. 

In  my  Cloud  Report,  Annual  Report  of  the  Chief  of  the 
Weather  Bureau,  1898-1899,  Volume  II,  chapter  11,  it  was 
shown  that  for  the  United  States  the  canal  theory  of  the  gen- 
eral circulation  of  the  atmosphere,  as  worked  out  by  Ferrel 
and  by  Oberbeck,  does  not  sufficiently  conform  to  the  obser- 
vations on  cloud  motions  to  be  a  satisfactory  solution  of  the 
problem.  The  Report  of  the  International  Committee,  1903, 
by  H.  H.  Hildebrandsson,  reached  the  same  conclusions  for 
nearly  all  parts  of  the  Northern  Hemisphere,  and,  therefore, 
that  canal  theory  may  be  finally  abandoned.  The  following 
paper  contains  some  suggestions  on  this  subject  which  seem 
promising,  and  adapted  to  laying  the  foundation  for  a  new 
development  of  this  branch  of  theoretical  meteorology.  The 
physical  facts  to  be  accounted  for  may  be  found  in  the  two 
publications  referred  to,  also  in  my  Papers  on  the  Statics  and 
Kinematics  of  the  Atmosphere  in  the  United  States,"  and  they 
need  not  be  recapitulated  in  this  place. 

THE    GENERAL    EQUATIONS    OF    MOTION. 

Referring  to  the  well-known  general  equations  of  motion  as 
summarized  in  the  AVeather  Bureau  Cloud  Report,  from  equa- 
tion (155)  we  have 

(1)  1  dP      dV      dut 

~  p  dx       dx        dt  ' 

1  dP  dV      rfu, 

p  dy  dy        dt 

I  OP  SV_dWi 

~  p  dz  dz   ~  dt 

These  are  transformed  into  the  first  form  of  polar  equa- 
tions (181),  these  again  into  the  forms  (200)  and  (201)  in  suc- 
cession, so  that  the  common  integral  becomes 


(2) 


dp        C  f 

->  =J  ( 


dv 


dw 


The  usual  method  of  development  proceeds  by  taking 
dx  dy  dz 


=      >    W  =     >        S°that 


f  _  dP  =   C(udu  +  vdv  +  wdw)  +V—0 


=  J?'  +  V-C. 

This  is  the  ordinary  form  of  the  equation  of  motion  on  the 
rotating  earth  as  given  in  treatises  on  hydrodynamics,  as  in 
Lamb,  p.  22,  and  Basset,  Vol.  I,  p.  34,  and  is  known  as  Ber- 
noulli's Theorem.  G  is  not  an  absolute  constant,  but  is  the  func- 
tion of  the  parameter  of  a  stream  line;  and  in  the  atmosphere, 
where  the  flow  takes  place  in  stratified  layers  having  different 
temperatures  and  angular  momenta,  it  changes  from  one  stra- 
tum to  another. 

It  is  also  possible  to  integrate  these  terms  along  an  arbi- 

trary line,  s=  I  ds  =  I  (dx,  dy,  dz),  and  in  this  case  the  deriva- 

tive relative  to  the  velocity  will  give  acceleration  along  ds  ; 
that  is,  we  have  qds  instead  of  qdq,  and  under  some  circum- 
stances this  may  prove  to  be  an  advantageous  method.  In 
meteorology  this  will  depend,  however,  upon  whether  the  one 

22  Monthly  Weather  Review,  Vol.  XXX,  pp.  13,  80,  117,  163,  250,  304,  347. 


or  the  other  set  of  terms  that  are  required  are  most  practically 
observed,  as  line  integrals  may  be  readily  computed  for  either 
of  these  systems. 

LINE    INTEGRALS    IN    THE    ATMOSPHERE. 

The  principles  of  the  canal  theory  of  circulation  have  been 
applied  by  V.  Bjerknes 23  and  J.  W.  Sandstrom  "  in  their  papers 
on  circulation,  under  the  form  of  line  integrals  around  arbi- 
trary closed  curves  in  the  atmosphere.  Thus,  the  circulation 
is  expressed  by  them,  with  the  vertical  and  horizontal  compo- 
nents of  the  total  enclosed  curve,  as 


Total 
circulation. 


Relative 
component. 


Earth's 
component. 


(5)  C7a  =     0       +  Ge 

(6)  fqds         =jVs    +2. 


dt 


ds      = 


(7) 
(8)   _ 


(9)   _  f*l  =  Cq 

•J       P  */ 


ds 


dS 


Equation  (7)  is  the  time  rate  of  change. 

(7a  =  the  line  integral  of  the  tangential  component  of  total 
velocity. 

G  =  the  line  integral  of  the  relative  velocity  (tangential). 

C  =  the  line  integral  of  the  velocity  of  a  point  on  the  moving 
earth  itself  (tangential). 

(9a>  1>  ?e)  =  ^e  velocities;  (q^  q,  qe)  =  the  accelerations. 

R  =  friction;  <"„=  the  angular  velocity  of  the  earth. 

P  =  pressure;  p  =  density. 

i  =  the  angle  on  the  plane  of  the  parallel  of  latitude  that  ds 
makes  with  the  direction  of  a  moving  point  of  the  earth. 

S1  =  the  projection  of  the  closed  curve  S  on  the  plane  of  the 
equator  for  the  polar  distance  0. 

These  integrations  involve  an  accurate  knowledge  of  the 
pressure,  density,  and  acceleration  at  numerous  points  along 
the  chosen  closed  curve,  and  this  it  is  very  difficult  to  obtain  by 
practicable  observations.  The  variation  of  »9  can  be  found  more 
readily.  Several  illustrations  are  given  by  the  authors  in  ap- 
plying the  theory  to  the  general  circulation  of  the  atmosphere 
and  to  the  local  cyclones  and  anticyclones,  but  these  illustra- 
tions do  not  seem  to  conform  satisfactorily  to  the  conditions 
observed  in  North  America,  as  will  be  set  forth  in  the  other 
papers  of  this  series  and  in  a  full  report  on  the  subject. 

There  arises  no  question  with  respect  to  any  of  the  terms  of 

the  equation  except  the  one  containing  -jp  which  appears  to 

be  an  addition  to  the  usual  form  of  the  equation  of  motion  on 
the  rotating  earth.  As  has  been  shown  by  V.  Bjerknes,  if  the 
angle  0  can  be  taken  constant  for  a  given  relatively  small 
closed  curve,  we  have 


=  2 


j 

,  cos  6  ,, 


/* 

J 


cos  i  ds, 


where  i  is  the  angle  that  the  element  ds  makes  with  the  par- 
allel of  latitude,  or  the  angle  between  the  two  radii  of  an  ele- 

"Meteorol.  Zeitschrift,  March,  1900;    April,  1900;    November,  1900; 
March,  1902. 

24  Ron.  Svens.  Vet.  —  Ak.  Handlingar,  Bd.  83,   No.  4;   Meteorol.  Zeit- 
schrift, April,  1902 ;  Vetens.  Ak.  1902,  No.  3. 

17 


18 


nientary  area,  as  shown  in  fig.  14.     Hence,  for  a  line  integral 
we  have, 

y 


(15) 


FIG.  14. — Component  axes. 

(IV) d    C  Cdw  C      di 

'  j  \  \  m  cos  i.  ds=  %J  -^-.  cos  i  ds  —  |  J  ^-^-  sin  i  as 

=  \(udy  —  vdx\, 


since0—  =  u,      m  —  =v,     dscoai  =  dy,     dseini=dx. 
dt  dt 

We  have  in  the  case  of  a  velocity  potential,  u  dy  —  v  dx  =  0; 
and,  as  is  well  known,  the  only  influence  of  the  rotation  of 
the  earth  is  to  add  a  deflecting  force  always  at  right  angles  to 
the  direction  of  motion.  The  integral  of  the  work  done  in 

moving  a  particle,  I  -J .  ds,  receives  no    additional  term  from 

the  fact  that  the  earth  rotates,  any  more  than  a  planet  alters 
the  velocity  in  its  orbit  from  a  force  perpendicular  to  its  path. 

We  thus  obtain  2  oi0  -,^  =  0,  and  all  the  developments  derived 

from  its  use  must  be  carefully  interpreted.  It  seems  impor- 
tant to  have  made  this  fact  clear,  in  order  that  the  equation 
used  as  the  basis  of  the  following  analysis  may  be  taken  with- 
out modifications.  If  the  gravity  potential  F=  gz  is  added 
we  obtain  the  complete  equation.  The  line  integral  of  a 
gravity  force  around  a  closed  curve  is,  also,  always  zero. 

EQUIVALENT   EXPEESSIONS    FOE    THE    DENSITY   p. 

1  P 

The  specific  volume  or  isoster,  —  =  v,  in  the  term   — ,  can 

P  P. 

be  discussed  in  four  different  ways,  and  substitutes  for  it  can 
be  introduced  into  the  equation. 

1.  From  Bigelow's  equation  (47a),  Cloud  Report,  we  have 


P     T  —          P   ^  '* 

where  the  variations  are  expressed  in  terms  of  />0,  P0,  P  and 
the  thermometric  temperature  t.  This  is  the  common  pro- 
cedure among  meteorologists. 

2.  From  equation  (75),  the  Boyle-Gay  Lussac  law  of  gases, 
(13)  1       RT  __ 

P~  p   ~v> 


where  R  is  the  gas  constant,  and  T0  =  #0  the  potential  tempera- 
ture. This  form  was  employed  by  H.  von  Helmholtz,  and  it 
has  several  advantages  over  the  others  in  applications  to  the 
atmosphere. 

4.  By  reducing  the  volume       to  unit  density  so  that  />0  =  1, 
we  shall  find  that 


P  ~  k-l  J  k     r 

which  is  the  form  used  by  Emden  in  his  paper  on  the  solar 
circulation. 

5.  The  potential  temperature  is  found  practically  from  the 
formula 

(")  /-v**-1  ,B 


Pi 

or  in  logarithms, 

(18)  '  log  0  =  log  00  +  0.2889  (log  B  -  log  B,). 

o>  dr 

DEVELOPMENT   OF    THE    TEEMS    —  ,    V,    AND    ,—  . 

Since  the  pressure    P  in  units  of  force  =  g0p,  we  have 
from  (15) 

(19)  P  *-*  _!  i-*  fc-i 
—  =  <7  »     *    R  .B .  n     k  r>  =   Q  TO    *    R.  9 .  n    k    • 

f*  ifO*0  +  -«  i'O*   0  * 

(20)  P_ 
p 

(21)  dP 


dr. 


. 

=   A  .  9  .  —       I   for   . 
dm 


d-P-=    A    9     ^ 
fidr  '    dr 


A  =  g0pa    k    R.  =   constant. 
/p\l=* 

•— •(*)'• 


k-l 

"       = 


The  gravity  potential,  including  the  centrifugal  force  of 
rotation  about  the  axis  z,  with  the  angular  velocity  <u0,  at  the 
distance  »  is,  for  the  positive  direction  of  r  outwards, 


(24) 


Hence  the  original  equation  (4)  is  transformed  as  follows: 
(25)  P_ 

P 
(26) 


.  i  (M»  _j_  u2  +  v?)  _  v+  G. 
ABi:  =  —  \  (u2  -(-  \?  +  twa)  -  £  i>02  +  ^-  +  C. 


where  the  variations  are  given  in  terms  of  R,  T,  p- — the  gas 
constant,  the  absolute  temperature,  and  the  weight — and  this 
has  been  used  in  some  discussions.  Since  the  atmosphere  is 
not  arranged  upon  the  adiabatic  law,  but  diverges  from  it  *•  ^<>K  __  ^  +  1  ( 

considerably,   this    method   must   be    cautiously  introduced,  #:     r 

though  there  is  a  strong  temptation  to  use  the  absolute  tern-     (29)     Second  stratum: 
perature  on  account  of  its  convenience. 

i 

1  /  50  \  *    1 

3.  Since  we   have  —  =  (  ^°  I    —  ,    by    equation    (84),    and 

P        \P  /     Po 
1          72  V7 

= 9 ,  by  (75),  we  obtain  the  third  form, 

Po        Po 

\       i  1  /„  \   *~  p  T» 


The  equations  of  motion  for  two  strata  flowing  over  each 
other,  and  having  different  potential  temperatures  and  angular 
momenta,  become, 
(28)     First  stratum: 


H'1 


At  the  discontinuous  surface  of  flow  the  pressure  rl  =  KV 
hence, 
(30)       /_!_       l\g0R'       ,   K'+O       ,   (V+V) 

e.     ' 


Po 


C      C 


e, 


.    , 

"' 


(u' 


19 


The  terms  in  u  and  w  may  not  always  be  neglected  where 
there  are  strong  meridional  and  vertical  currents,  as  in  cyclones 
and  anticyclones. 

TO    FIND    THE     DIRECTION    OF    THE     BOUNDARY    CURVE     BETWEEN     TWO 

STRATA. 

1.  Differentiate  (27)  for  r  with  m  constant. 


Then,  in  crossing  the  boundary  from  the  first  to  the  second 

stratum, 

(32) 


dr 

2.  Differentiate  for  m  with  r  constant,  at  the  same  time 
holding  the  angular  momentum  (via)  constant  in  each  stratum. 
Equation  (27)  can  be  written: 


Differentiating, 
(34)  Q  = 


du 


udu       wdw\ 

1 ). 

dm         dm  I 


wdw 
dm 


For  the  two  strata, 
(36)  <?(*.-».)       1  /V- 

dm         ~  m\      « 


udu       wdw\    1 


/wrfit       MH/M>\    1 

~     + 


omitting  terms  of  the  second  order. 

3.  Finally,  dividing  (36)  by  (32),  we  obtain, 
(37) 


dr 


1 
gw 


This  equation  defines  the  slope  of  the  curve  which  separates 
the  two  stratified  currents  that  flow  past  each  other,  preserving 
their  angular  momenta,  Q  =  vm  =  <onr2  =  constant,  according 
to  the  vortex  law,  where  (u  is  the  total  angular  velocity  upon 
the  rotating  earth  and  m  is  the  distance  from  the  axis  of  rota- 
tion. It  can  be  written  and  interpreted  in  three  different  ways, 
and  this  gives  rise  to  three  cases,  each  of  which  finds  its  appli- 
cation in  atmospheric  circulations.  The  equations  given  in 
the  papers  by  von  Helmholtz  and  by  Emden  can  be  readily  trans- 
posed into  Case  I  and  Case  III,  but  Case  II  has  not  been  con- 
sidered heretofore.  Omitting  terms  in  u  and  w,  these  three 
cases  may  be  expressed  as  in  equations  (38),  (39),  and  (40), 
following. 

CASE  I.    APPLICABLE    TO    THE  TEMPERATE  AND    POLAR  LATITUDES  OF  THE 

EARTH. 

.  >  v.~l  eastward 


and 


•  IT, 


for 


relative 
velocities. 


(38)     +  dr 


+  dr  r(v22  —  v02)  0,  —  (y,2  — i>02)  i 

—  dis  \_  #j  —  8t 

The  second  member  of  the  equation  is  positive  if 


where  va  >  v0,  v2  >  v0,  v1  >  vv  and  61  >  #2,  that  is  to  say,  if  the 
higher  strata  have  a  higher  potential  temperature  and  greater 
eastward  relative  velocity  than  the  lower,  the  quantities  being 
arranged  as  in  fig.  15. 


Fia.  15.— Case  I. 

Take  a  point  in  the  atmosphere  defined  by  (r,  m)  the  radius 
and  the  radius  of  rotation,  respectively.  The  next  successive 
point  on  the  line  of  separation  of  the  two  gyrating  strata  is 
given  by  (r  +  dr),  (m  —  dm)  as  indicated,  so  that  the  curve 
continually  rises  above  the  successive  tangents  to  the  horizon, 
but  approaches  the  axis  of  rotation  in  the  direction  of  the 
celestial  pole.  Since  (D*  —  v02)  is  the  square  of  the  relative 
linear  eastward  velocity,  it  follows  that  the  strata  in  the  atmos- 
phere subject  to  this  law  have  a  continually  greater  eastward 
drift  and  greater  potential  temperatures  with  the  increase  in 
altitude  above  the  surface.  These  conditions  are  character- 
istic of  the  earth's  atmosphere  beyond  a  certain  latitude  which 
varies  with  the  height  above  the  surface.  The  Weather  Bureau 
Cloud  Keport,  1898,  proved  that  the  velocities  and  also  the 
potential  temperatures  for  the  United  States  conform  to  Case 
I,  as  in  chapters  12,  13,  and  14,  which  contain  a  discussion  of 
the  departure  of  the  temperatures  of  the  upper  strata  from  the 
adiabatic  law  in  the  sense  that  these  strata  are  overheated. 
Those  velocities  have  been  properly  prepared  for  immediate 
introduction  into  the  above  formula. 

CASE  II.  APPLICABLE  TO  THE  TROPICAL  ZONES  OF  THE  EARTH. 


»,< 

(39)    — dr 


and- 


.v-v 


for 


K 

h 

K 


<  u0~|  westward 

<  o0    relative 
>  i>2J  velocities. 


The  second  member  of  the  equation  is  negative  if 
,  2 
L,  where  t\  <  «0,  u,  <  va,  w,  >  vv  and  0,  <  02, 

that  is  to  say,  if  the  higher  strata  have  lower  potential  tem- 
peratures than  the  lower,  and  the  lower  strata  a  greater  west- 
ward relative  velocity  than  the  higher,  the  quantities  being 
arranged  as  in  fig.  16. 

Take  a  point  in  the  atmosphere  defined  by  (r,  GJ)  and  the 
next  successive  point  on  the  line  of  separation  is  given  by 
(r — dr),  (m — dm),  as  indicated,  so  that  the  curve  continually 
falls  below  the  successive  tangents  to  the  horizon,  and  ap- 
proaches the  axis  of  rotation  in  the  direction  of  the  celestial 
pole.  The  relative  velocity  is  westward,  since  v0  is  greater 
than  vl  and  v2,  so  that  v*—va*  and  v22 — 1'02  are  both  negative 
quantities.  Since  u,2 — u02  is  a  smaller  negative  quantity  than 
r22 — «02,  the  numerator  is  negative.  Also,  the  denominator  is 
negative,  for  6l  <  #2.  These  conditions  are  fulfilled  in  the 
tropical  zones  where  the  westward  drift  is  greater  in  the  lower 
strata  and  diminishes  upward,  while  the  potential  tempera- 


20 


FIG.  16.— Case  II. 

tures  decrease  upward.  Chapter  8  of  the  full  report  will 
discuss  the  velocities  in  the  tropical  zones  of  the  West  Indies. 
The  potential  temperatures  in  the  Tropics  still  remain  to  be 
computed. 

CASE    III.       APPLICABLE    TO    THE     ATMOSPHERES     OF     THE    SUN,    JUPITER, 

AND   SATURN. 

««_««       v'-v1         [vi  >  VI  eastward 
9l  >  #2  and    '  g     -  <    *  g     -  for     u2  >  «„    relative 

1  *  Lvi  <  vzJ  velocities. 

(40)  j-dr  =  _    T^  r«-<)  g.  -(V-Q  02"|  =  _ 

The  second  member  of  the  equation  is  negative  if 

„«_,,»       v'—v' 

g       >       g     »  where  w,  >  •«„,  t;.,  >  «0,  v,  <  u,,  and  0,  >  02, 

that  is  to  say,  if  the  higher  strata  have  a  higher  potential 
temperature  and  a  smaller  eastward  relative  velocity  than  the 
lower,  the  quantities  being  arranged  as  in  fig.  17. 


FIG.  17.— Case  III. 

Take  a  point  in  the  atmosphere  denned  by  (r,  m),  and  the 
next  successive  point  on  the  line  of  separation,  which  has  vary- 
ing temperatures  but  angular  momenta  that  are  constant  within 
the  thin  layers,  is  given  by  (r+dr)  (uo  +  dvo),  as  indicated,  so 
that  the  curve  continually  rises  above  the  plane  of  the  horizon, 
and  recedes  from  the  axis  of  rotation  in  the  direction  of  the 
celestial  pole.  The  warmer  strata  are  nearer  the  axis,  and  the 
potential  temperature  increases  in  the  direction  parallel  to 
the  axis  of  rotation,  and  at  the  same  time  the  relative  velocity 
is  such  that  the  strata  near  the  pole  rotate  more  slowly  than 
those  at  greater  distances.  These  conditions  are  found  to 


prevail  in  the  atmospheres  of  the  sun,  also  of  the  planets  Jupi- 
ter and  Saturn,  as  attested  by  the  belt  formations  and  the 
systems  of  vortices  penetrating  to  the  surface.  On  the  sun 
the  granules  of  the  photosphere  are  the  ends  of  vortex  tubes 
between  adjacent  strata  having  different  velocities.  Similar 
vortex  tubes  are  seen  on  the  two  planets. 

THE    INTERACTION    OF     CASE    I    AND    CASE    II     IN     THE     EARTH 's     ATMOS- 
PHERE IN  THE  FORMATION  OF  LOCAL  CYCLONES  AND  ANTICYCLONES. 

In  the  earth's  atmosphere  the  boundary  between  the  east- 
ward drift  of  the  temperate  zones  and  the  westward  drift  of 
the  tropical  zones  is  an  arch  spanning  the  equator  high  up 
into  the  cirrus  cloud  strata,  and  resting  on  the  surface  at  lati- 
tudes 30°  to  25°.  On  the  poleward  side  Case  I  applies  but  on 
the  side  toward  the  equator  Case  II  prevails. 

If  the  circulations  of  Case  I  in  the  temperate  and  polar 
zones,  and  of  Case  II  in  the  tropical  zones,  are  applied  without 
further  conditions,  the  isobars  in  the  atmosphere  will  be  dis- 
tributed, as  in  fig.  18,  so  that  they  rise  from  the  arched  boun- 
dary of  the  eastward  and  the  westward  relative  velocities 
toward  the  pole  and  toward  the  plane  of  the  equator  re- 
spectively. This,  however,  is  not  the  course  of  the  surfaces 
of  pressure  in  the  atmosphere  as  determined  by  the  observa- 
tions near  sea  level,  and  by  computations  at  higher  levels. 
To  illustrate  the  actual  conditions,  in  fig.  20  Ferrel's  values 
of  the  isobars  on  the  sea  level  are  given  from  pole  to  pole, 
and  Sprung's  isobars  for  the  2000-meter  and  the  4000-meter 
planes.  The  practical  problem  is,  therefore,  to  account  satis- 
factorily for  the  modifications  of  the  types.  In  the  present 
state  of  meteorology  we  enter  upon  a  field  that  is  incompletely 
explored,  so  that  the  following  remarks  are  suggestive  of  the 
solution  rather  than  final,  but  there  will  be  much  material 
that  sustains  them  in  the  complete  report,  Volume  II,  Report 
of  the  Chief  of  the  Weather  Bureau,  1903-1904. 

There  are  two  conditions  that  modify  the  solutions  of  Case 
I  and  Case  II  very  decisively.  (1)  The  first  is  that  the  as- 
sumption that  the  angular  momenta  in  the  several  strata  re- 
main constant  around  the  earth,  or  that  the  air  rotates  in 
unbroken  rings,  does  not  hold  good  even  approximately.  Be- 
sides the  waves  and  vortices  engendered  between  discontinu- 
ous strata,  as  von  Helmholtz  explained,  there  is  a  yet  more  pow- 
ful  cause  for  the  breaking  down  of  the  vortex  law,  v  as  =  con- 
stant, namely,  in  the  cyclones  and  the  anticyclones  of  middle 
latitudes,  and  in  the  convectional  vertical  circulation  near  the 
equator.  (2)  The  second  is  that  the  boundary  between  the 
eastward  and  the  westward  drift  does  not  girdle  the  earth 
uniformly,  but  is  broken  up  into  sections  by  the  intrusion  of 
Case  II  into  the  region  of  Case  I,  and  the  extension  of  Case 
I  into  the  region  of  Case  II,  so  that  the  high  pressure  belt 
which  this  solution  assumes  to  encircle  the  earth  is  broken  up 
into  large  isolated  high  areas  or  centers  of  action,  as  those 
lying  over  the  oceans  in  summer,  or  over  the  continents  in 
winter,  in  the  lower  strata  of  the  atmosphere.  To  work  out 
the  theory  of  these  details  will  be  a  large  task  for  the  meteor- 
ologist of  the  future.  These  two  types  of  disturbance  oper- 
ate together,  somewhat  as  described  in  the  Weather  Bureau 
Cloud  Report,  1898-1899,  so  that  the  present  paper  is  merely 
an  extension  of  the  analysis  there  suggested.  The  following 
descriptive  statement  attempts  to  outline  the  probable  course 
of  the  modifications  of  the  pure  vortex  theory  contained  in 
the  system  of  equations  given  above. 

Referring  to  figs.  18  and  19,  the  "unmodified"  and  the 
"modified"  systems,  respectively,  it  is  evident  that  the  solar 
radiation  in  the  Tropics,  if  unrelieved,  will  by  accumulation 
raise  the  isobars  of  Case  II,  by  increasing  the  potential  tem- 
perature #2  and  the  westward  velocity  v3  —  v0  in  the  lower 
strata.  In  a  circulating  atmosphere  the  relief  comes  in  two 
ways,  (1)  by  forming  a  vertical  convection  near  the  equator, 
and  (2)  by  forcing  a  horizontal  convection  into  the  lower  strata 


21 


Case  I. 


Case  IT. 


CaseJT. 


Cause.  I. 


FIG.  18. — Cases  I  and  II  unmodified. 

of  the  temperate  zones.  The  first  transports  heat  into  the 
upper  strata,  reducing  #2  and  increasing  #,,  so  that  the  west- 
ward drift  diminishes.  At  the  same  time  the  intrusion  of  masses 
of  air  having  one  value  of  momentum  (mv)n  into  those  having 
another  value  (mv).^  will  change  their  velocities.  These  two 
causes  lower  the  lines  of  Case  II  011  the  equator  side,  and  in 
the  lower  strata  may  even  reverse  them.  Accompanying  these 
changes  a  component  on  the  meridian  toward  the  equator  sets 
in,  so  that  the  trades  from  the  northeast  and  southeast  are  de- 
veloped, and  the  first  minor  circulation  is  maintained  in  the 
sense  indicated  by  the  arrows  over  the  tropical  zone  of  fig.  19. 
The  rise  and  fall  of  the  isobars  of  Case  II,  with  the  relief  of 
the  incoming  solar  heat  through  this  circulation,  is  a  complex 
but  sensitive  form  of  natural  heat  governor  which  is  self- 
regulating,  and  preserves  the  normal  state  of  equilibrium 
proper  for  the  season  of  the  year.  This  special  action  is 
chiefly  due  to  the  mutual  movement  among  the  terms  of  equa- 
tion (39)  for  Case  II. 

A  still  more  complex  system  relates  to  the  temperate  zones 
and  Case  I.  To  some  extent  the  terms  within  equation  (38) 
for  Case  I  go  through  a  similar  self-adjustment  in  response  to 
the  local  insolation,  but  this  is  by  no  means  the  primary 


Case  I  +  Ca.se  H 


Oasel . 


Ca.se  H+  Ca.se! . 


Casel+Ca-Bett. 


FIG.  19.— Cases  I  and  II  as  modified. 

cause  for  the  depression  of  the  isobars  of  fig.  18  to  those  of 
fig.  19.  As  explained  in  my  paper,  "  The  mechanism  of  coun- 
tercurrents  of  different  temperatures  in  cyclones  and  anti- 
cyclones," MONTHLY  WEATHEH  REVIEW,  February,  1903,  cyclones 
and  anticyclones  are  formed  by  horizontal  currents  under- 
flowing  the  prevailing  eastward  drift.  Thus,  as  shown  on  fig.  19, 
warm  currents  flow  from  the  Tropics  into  the  Temperate  Zone, 
as  from  the  Gulf  of  Mexico  into  the  United  States,  underneath 
the  eastward  drift,  and  this  stratification  of  warm  air  beneath 
cold  air  produces  two  changes.  The  potential  temperature 
#2  is  increased,  the  value  9l  —  #,  is  diminished,  the  velocity  is 
checked  and  the  isobars  fall,  because  the  angular  momentum 
is  diminished.  At  the  same  time  that  the  air  rises  on  the  east 
side  of  the  cyclone,  a  cold  current  from  the  north  flows  to  the 
west  side,  and  this  decreases  its  #2  but  increases  the  difference 
#j  —  02,  so  that  the  velocities  are  increased.  It  is  known  that 
the  eastern  warm  current  tends  to  curl  westward  and  the 
western  cold  current  tends  to  curl  eastward  about  a  cyclonic 
center;  inverted  conditions  prevail  around  an  anti cyclonic 
center.  Furthermore,  the  dynamic  action  of  intruding  cy- 
clones and  anticyclones  from  the  lower  to  the  higher  strata, 
by  their  interchange  of  inertia  with  the  eastward  drift,  must 
diminish  the  eastward  velocity  and  lower  the  isobars  of  Case  I. 


•7Z772. 
47O 


4OOO        }6O 

tte 


20OO 


.Surface 


60O 
590 
seo 


76O 
7JO 
-140 


+70°     +6O°     +SO°    +4O°   +30°    +20°    f-JO" 


O°  •  —JO"     —ZO°    -JO°    - 


—5O°    -6O°    —7O°    -8O°    —9O° 


Fio.  20. — Pressures  at  different  latitudes  (Ferrelj  and  altitudes  (Sprung). 


22 


This  effect  of  the  interchange  of  components  may  be  seen  by 
combining  the  terms  of  Case  I  and  Case  II  algebraically. 
Thus,  we  have,  symbolically, 


_-dw_    Case  I 


~" 


[= 


-dr 


Jrdecrease  of  (+dr) 
Case  II        Lincrease  of  ( — dnj) 


1 


so  that  the  lines  of  Case  I  are  plotted  nearer  the  axis,  and 
lower  in  the  atmosphere  above  the  horizon  than  in  fig.  18. 
There  are  instances  in  which,  by  this  intrusion  of  the  warm 
air  of  Case  II  from  the  Tropics  into  the  region  of  Case  I,  the 
potential  temperature  of  the  lower  strata  is  greater  than  that 
of  the  higher  strata,  so  that  Case  II  supersedes  Case  I  in  the 
temperate  zones  with  local  westward  winds.  Similarly,  the 
interplay  of  these  cases  outside  their  normal  regions  is  a  suf- 
ficient cause  for  the  manifold  local  circulations  found  in  the 
lower  strata  of  the  atmosphere  up  to  about  3  miles  from  the 
ground,  beyond  which  the  circulation  is  more  regular.  The 
amount  by  which  the  normal  lines  of  Case  I  are  depressed 
through  the  intermixture  of  Cases  I  and  II,  in  consequence  of 
temperature  and  inertia  interchanges  in  the  lower  strata, 
measures  the  amount  by  which  the  vortex  law  ceases  to  be 
complete  in  its  application,  and  by  which  the  Ferrel  theory 
of  the  general  circulation  becomes  an  untenable  hypothesis. 
In  effect  these  interchanges  are  attended  by  secondary  currents 
along  the  meridian  so  that  there  is  a  second  minor  circuit  in  the 
temperate  zones,  somewhat  as  indicated  on  fig.  19.  The  H,  L,  H, 
of  the  vertical  section  should  be  understood  to  stand  over 


H,  L,  H,  on  the  horizontal  plane  of  the  given  latitude;  that  is, 
they  are  not  distributed  in  latitude  but  in  longitude,  and  should 
be  superposed  in  a  correct  projection.  So  far  as  I  understand 
the  facts,  this  circulation,  taken  in  connection  with  the  tropical 
circuit,  conforms  to  the  results  of  the  International  Survey,  as 
stated  in  H.  H.  Hildebrandson's  Keport,  which  need  not  be 
here  recapitulated.  In  the  polar  zone  our  information  is  too 
meager  to  afford  us  very  definite  knowledge,  but  I  suspect 
that  there  is  a  third  circuit  as  shown  in  fig.  19,  though  it  may 
not  be  very  pronounced  and  well  defined. 

It  is  my  purpose  to  work  out  the  data  for  the  temperate  and 
the  tropical  zones  now  in  the  possession  of  the  Weather  Bureau 
and  applicable  to  the  North  American  Continent,  along  the 
lines  here  indicated.  The  attempt  to  bring  these  laws  of  the 
general  and  the  local  circulations  into  a  harmonious  numerical 
scheme  will  require  considerable  labor,  but  it  is  believed  that 
it  can  be  accomplished.  The  data  contained  in  my  reports, 
while  apparently  somewhat  disconnected,  are  in  reality  all 
contributory  to  my  solution  of  the  problems  of  atmospheric 
circulations  both  of  the  earth  and  of  the  sun,  together  with 
the  connections  between  them.  It  is  proper  to  determine  care- 
fully the  separate  portions  of  the  work,  i.  e.,  the  velocities  and 
temperatures  of  the  strata  in  motion  as  dependent  upon  obser- 
vations, before  trying  to  put  them  together  in  a  final  synthesis. 
It  is  only  necessary  to  have  in  mind  the  general  plan  of 
development,  as  here  outlined,  in  order  to  keep  the  several 
portions  in  harmonious  relations  with  each  other. 


IV.— VALUES  OF  CERTAIN  METEOROLOGICAL  QUANTITIES  FOR  THE  SUN. 


THE  IMPORTANCE  OF  THESE  VALUES  TO  TERRESTRIAL  METEOROLOGY. 

The  most  important  data  needed  for  use  in  studies  in  solar 
physics  are  the  correct  values  of  the  pressure,  the  temperature, 
the  density,  the  gas  constant,  and  their  many  derived  rela- 
lations,  at  the  surface  of  the  sun,  within  its  mass,  and  through- 
out the  gaseous  envelope.  In  the  present  uncertain  state  of 
our  knowledge  of  these  quantities,  even  an  approximate  deri- 
vation of  these  data  is  important,  and  this  forms  the  justifica- 
tion for  the  studies  contained  in  this  paper.  The  problems  of 
the  circulation  within  the  sun's  photosphere,  the  transitions 
and  the  transformations  in  the  atmospheric  envelope  with  the 
attendant  radiations  and  absorptions,  the  heat  and  light  re- 
ceived at  the  outer  surface  of  the  earth's  atmosphere,  the  re- 
sulting absorption  and  transmission  of  energy  in  the  air,  and 
the  dependent  circulation,  are  all  languishing  for  the  lack  of 
a  sound  footing  for  our  computations  and  deductions.  The 
computations  for  the  surface  temperature  of  the  sun  give 
results  ranging  from  5000°  to  10,000°;  using  Bitter's  Law, 
Professor  Schuster  computes  the  temperature  at  the  center  of 
the  sun  as  12,000,000°,  assuming  that  it  is  composed  of  hy- 
drogen split  up  into  mouatomic  elements.  But  it  is  evident 
that  any  such  range  of  temperature  would  simply  explode  the 
sun,  whereas  it  now  circulates  in  a  moderate  manner.  Unless 
some  value  for  the  temperature  of  the  solar  photosphere  can 
be  found,  it  will  be  impossible  to  determine  what  percentage 
of  the  total  solar  radiation  is  absorbed  in  the  solar  envelope, 
even  though  the  radiant  heat  be  computed  successfully  on  the 
outer  surface  of  the  earth's  atmosphere  from  radiation  meas- 
urements at  the  ground.  Should  the  following  remarks  prove 
to  be  merely  suggestive  it  will  be  proper  to  make  them  as  a 
contribution  to  the  problems  in  solar  physics. 

I  have  been  interested  in  the  paper  by  Prof.  F.  E.  Nipher, 
on  the  "Law  of  contraction  of  gaseous  nebulae,"25  because  it 
seems  to  offer  a  way  of  escape  from  the  impossible  results 
which  follow  from  Bitter's  equations,  where  the  exponent  in 
P  vn  =  B  is  1.33  -f .  Nipher  makes  the  value  of  n  =  1.10,  and 
from  this  exponent  the  entire  system  of  relations  seems  to  be 
more  probable.  I  will  recapitulate  Nipher's  equations,  after 
making  the  following  changes  in  his  notation  to  reduce  them 
to  the  symbols  used  in  my  papers: 

Nipher.  Bigelow. 

Gas  constant  change  C  to  R 

Density  "       S    "  /> 

Distance  from  center  "       R   "  r 


Mechanical  equivalent  of  heat 

J  "  A' 

1 

Heat  equivalent  of  work 

1 

«     A 

J     * 

1 

Constant 

"      A    "  B 

Batio 

"       p    "  b 

Constant 

"       k    "  k' 

"Transactions  Academy  of  Science,  St.  Louis,  October  1,  1903. 


NIPHER  S    EQUATIONS. 

Adiabatic  law  for  perfect  gases: 
741)     Pv=RT. 
Heat  relation: 

Assumed  laws  for  non-perfect  gases: 

(43)  Pvn=Pav"=B. 

(44)  IV--*. 


(46)        js=i  = 

Specific  heat: 


AR 

Gravitation : 

(47)  ~-=—kt^fp  =  —  k'1- 
ar  r'  ' 

Pressure : 

(48)  P 


4.19  x  10' 


_ 

1.5173x10' 


[2        -1     n  r  -il. 

*"-3»'  .  Bn  r  "    °-9551'8' 
(2-n)'     2TF~?J  l^FpJ 


T'      0.636  M '  k' 


Density: 

[In  — Sri*  B      1J_       f  0.955  I1-11 

(49)         /)  =      -r~ r?   •  ,     2-"=      j—j. 

=  0.95 
Temperature : 


R  T         0.78  M 


(50)      T 


11  /  0.95  W" 


=  0.818 


5     |    (2-n)s      2^/P 
Jf*« 


R 


Mass : 


2-n 


n  -  3n2)  1  -A 
• 


P(2 


3n2)  1  -A-     £J« 
-n)'J  '•'••'••' 


0.955V-" 


0.77 


2-n 


1.22 


Tr 


23 


24 


Weight  of  one  gram  at  the  surface: 
k*  M                 1  2  —  n  \\   B(4:n  —  3n')  h-n     1 

»     .  ™T             2flr 

Auxiliaries. 
/dQ\                       "(dv\   (dP\           dP               d" 

R  M     R  M 

-  cP-A  lp           v 

,f,-AKit-               ?  —  r^.* 

dy                2      dr 
-S+*^*                               V=  +  2-n-r' 

A  R 

-2-n         r           L22     r 
Auxiliaries  : 

,3)    n-r»-  2n^_  3  j    (     R 

1  —  ?i 

2c..  -f  4^4  7J      6K  —  4 
/  r-,7  \                „           8_J                 .                     1  10 

^(4  —  3n)>i  J 
f(4/t  —  3/i*)lf"|  —  — 

2<-p  +  3A  R      5/c  —  3 

3;z  —  4                   K                   4  —  3c 
(68)              Cj,  =  A  R  g  _  2ft  =  .4  7.'  K  _  l  =  A  R  ^  _  l  . 

4                  2  —  n     M  L*                 M  /c2 

»•  (initial) 

Contraction  ratio  o  —    .    ("final1)   ' 

f                           /r  V 
(55)     P=P0(^j    =P06*. 

/r  \3 

(56)     p=r\-?)  =  />.*• 

\oi  )     -f         *  \  r  /   '       ° 
Mass  : 

4       ,                  2  —  n        j 

[58)         Jf=ij-  -r  •/>„=   ="4_3ft^'»' 

Average  density: 
f  ro\                T                       ^           ^                   n                               3  86  n 

(OJ)                      11     J.    1       V   r.    X     1       2      o            U.O1O        n           . 

Heat: 

(70)               0  =  (%y\    (T  -  T0)  =  -  (c,  +  4J  7?)  (T  -  2T0) 

(c,  +  ±A  R)  T0  (b  -  1). 
Work: 

(71)              W=    CP  do=P0  'i^J*"    ^  =  r^n  (b  -  1) 

/>oo    ,                4  —  3n  M'li*              „  3f'^ 
=  4-Jr    '-2pd?'=       „          2r     =°-636     2r    ' 
Ratios  : 

/7O\j-i.               £_  Z                                  P'                                                     07^ 

l«"^     ia          4  —  3^    2-n            4  —  on 

Distance  from  center  to  stratum  where  the  density  />  =  aver- 
age density  pa: 

-  w  '    cv  +  cp  +  ±A  R      2cv  +3A11      5/c  —  3 
0           CB  -f  4^  R              cv  +  4A  R 

/7Q\                                _     P     '                                    -     '                                                                 Q  AA 

4  3W       —  j— 
r                                                  0.545?-. 

T^ 

(74)               n       5K       3                                                              400 

3  (2  —  n) 
Average  pressure: 

4s  j    r2  P  dr           „ 
(611     P  —      ^  °               —3P—                           f>40  P 

Differences: 

/7K\                                                                                     /IP                            A1  8  A  A    T> 

v  *"*•  /                            s*f                        £*  Kj, 
4-  J    r1  dr 

J  o 

Distance  from  center  to  stratum  where  the  pressure  P  = 
average  pressure  P0: 

[~|  2-" 
1    6  —  5n      2»                                                    Q  502 

(75)     cp      ^-3(2-n)J      5/c  -3      J*'K 
1           4  —  3n      3/  >P  J 

~  5*c  —  3          n            %r    Ta 

For  a  rise  of  1°  C.,  energy  equivalent  to  2cp  +  3^4  R  heat 
units  must  be  applied  to  the  unit  mass,  of  which  cp  +  4^4  R 
heat  units  are  radiated  per  unit  time,  and  cp  —  A  R  =  cv  heat 
units  are  used  in  raising  the  temperature. 

THE   ASTRONOMICAL    CONSTANTS   FOB    THE    EAETH    AND    THE    SUN. 

It  is  difficult  to  select  from  the  available  astronomical  data 
a  system  of  constants  that  is  rigorously  self-consistent,  and  in 
this  preliminary  discussion  it  is  not  necessary  to  make  com- 
plete adjustments  between  the   several  quantities.     The   fun- 
damental units  employed  are  conveniently  the  C.  G.  S.  system, 
and  not  the  C.  S.  system,  because  in  the  thermodynamic  for- 
mulae the  unit  of  mass  is  the  gram.     In  the  C.  G.  S.  system 
the  gravitation  constant  is  found  from  the  formula, 
M  m                           R1  n 

/rff*\                                            „              7,2         1            C3r\  4-V»  o  41    /-'^                1    i'O 

~R~f                     ~M^n' 
The  constant  for  transformations  from  the  C.  S.  system  to  the 

C.  G.  S.  system  is      ;  i.  e.,  (mass  C.  S.)      =  (mass  C.  G.  S.). 

K                                                1C 

3     2-nJ 

Average  temperature: 
(63)     T   —  3      '              T  —                                                   1.08  T. 

Distance  from  center  to  stratum  where  the  temperature  T  = 
average  temperature  Ta: 

(64)     r  —         .                      ~l>r  —                                         0  707  r 

Specific  heat: 
dP          dv 
dO             **  P        ^  u       c  —  71  c        c    /K  —  ?i\ 

^      '        dT               dP      do             1  —  n          K   \i  —  n)' 
~T+    v 

25 

TABLE  7.  —  Astronomical  constants. 

Hence, 

Numbers.            Logarithms. 

K 

Rt   zz  mean  radius  of  earth,  Bessel's 

6370  19100cm.       8.8041525 

~  m  ^' 

spheroid 

R^  = 

17.  6083050 

This  asserts  that  if  —  remains  constant,  v  =  —  also  remains 

R*  = 

26.  4124575 

m                                            f> 

pal   zz  average     density     of    earth, 

5.  576      0.  746323 

constant.      If  a  gas,  as  hydrogen,  />  =  0.000089996,  is  sub- 

Harkness 

jected  to  the  same  relative  increase  in  P  and  T,  it  remains  at  the 

4  

4.  1888      0.  622089 

K 

3   " 
i 

same  density  as  that  for  which  its  gas  constant       was  computed. 

MI  ~  ~ir  Rf  pa,  zzmass  of  the  earth 

6.  0377  X  ISO27  27.  78070 

We  can,  therefore,  transform  hydrogen,  or  other  perfect  gases, 

in  grams 

from  terrestrial  to  solar  conditions  by  simply  multiplying  by 

m    —  1  gram 

1.  00      0.  000000 

the  proper  factor.     In  this  case  it  will  be  x  =  28.028,  the  ratio 

<70    zz  acceleration     per    second    at 

980.60cm.      2.991492 

of  g  at  the  surface  of  the  sun  to  g0  at  the  surface  of  the  earth. 

surface  of  earth 

In  Eclipse   Meteorology  and  Allied    Problems,   chapter  4, 

R  *  n 

i 

Table  14.  —  "Fundamental  constants,"  a  series  of  values  was 

1?    —  5j  Jo  —  constant 

2  818927— 

computed  depending  upon  assumed  values    of  r,  the   sun's 

J/,  m 

1.  5173  x  10' 

j 

radius,  and    G,  the  ratio  between  gravity  at  the  surface    of 

zz  transformation  constant 
ft2 

1.  5173  X  10'      7.  181073 

of  Mie  sun  and  gravity  at  the  surface  of  the  earth.     Since  these 

values  have  been  changed  a  little  in  the  preceding  computa- 

— ratio  of  mass  of  sun  to  mass  of 

333432.        5.  523008 

tions,  it  will  be  necessary  to  reconstruct  the  numerical  values 

J  i                     earth,  Newcomb 

of  that  table,  although  the  effect  upon  the  dependent  quanti- 

M  =  mass  of  the  sun 

2.  0132  X  1033     33.  303878 

ties  is  not  important.     In  order  that  the  transition  from  ter- 

r     zz  radius  of  sun  for  Auwer's  di- 

694800 80000cm.     10.8418603 

restrial  to  solar  conditions  may  be  made  as  plain  as  possible 

ameter  (31'  59.26") 

to  the  reader,  we  will  compute  the  fundamental  constants  on 

r2     zz 

21.  6837206 

the  supposition  that  the  earth  is  surrounded  by  a  hydrogen 

ri     — 

32.  5255809 

atmosphere  instead  of  the  common  air,  making  allowance  for 

p     —  parallax  of  the  sun,  Newcomb 

8.7965"       0.9443099 

the  change  in  density. 

D    zz  distance  from  sun  to  earth      1493  40870  00000  cm.     13.  1741786 

r/D     i-'ti  ir.   r\f  voflii                                                                                                 -i  r\n    rv+1            n    /-vorrrrrvfTo 

TABLE  8.  —  Constants  for  one  atmosphere  of  hydrogen  on  the  earth. 

/rt[  —  Liino  oi  rauii 
S/S,  —  ratio  of  surfaces  (109.  071  )2 

iuy.u/j.       a.uoMUfo 
11896.4      4.0754156 

Formulae.                     M.  K.  S.  system.            C.  G.  S.  system. 

V/  F,  rz  ratio  of  volumes  (109.  071)3 

1297548.       6.  1131234 

^,    gravity  at  surface  of  sun       . 

'         28  028      1  4475924 

Loga-                               Loga- 

gravity  at  surface  of  earth         j 

Numbers.       rithms.        Numbers.        rithms. 

pn    zz  mean  density  of  the  sun  zz 


M      /J,3 

J/!  '   r< 


1.43287      0.156208 


(  18.  5212  miles/sec, 
velocity  of  the  earth  in  its  orbit  •) 

I  29.80670  cm./sec. 


1.267670 
6. 474314 


zz       —  acceleration  at  the  dis- 
tance of  earth 


(check) 


zz  J/  =  rate  at  which  earth  falls 
toward  sun 


0.  59491  cm./sec.       9.  774448—10 
0. 23422  inch/sec.     9.  369615—10 


0.  29746  cm./sec. 
0. 11711  inch/sec. 


9. 77448—10 

9.473418—10 
9.  068585—10 


APPLICATION     OF     THE      THERMODYNAMIC      FORMULAE      TO      THE     GASEOUS 
ENVELOPE    OF    THE    SUN. 

The  evidence  from  the  action  of  the  lines  in  the  solar  spec- 
trum, as  regards  shifting,  broadening,  and  reversals,  shows 
that  in  the  envelope  resting  upon  the  photosphere,  comprising 
in  its  contents  the  reversing  layer,  the  chromosphere,  and  the 
inner  corona,  the  gases  may  be  treated  as  approximately  per- 
fect gases  and  tending  to  conform  to  the  Boyle-(Mariotte)- 

Gray- Lussac  law,  P  v  =  ---  T,  where  P  is  the  pressure  in  units 

of  force,  v  the  volume,  K  the  absolute  gas  constant,  m  the 
molecular  weight,  and  T  the  absolute  temperature.  I  propose, 
also,  to  apply  the  same  law  to  the  solar  mass  within  the  pho- 
tosphere, with  a  suitable  modification,  and  to  compare  the 
results  with  the  data  obtained  from  the  use  of  Professor 
Nipher's  equations.  We  can  first  multiply  the  equation  by 
any  numerical  value,  x,  and  distribute  the  variation  between 
P  and  T  alone,  holding  the  density  identical  in  the  two 
conditions. 


Formulae. 

M.  K.  S.  system. 

C.  G.  S.  system. 

Loga- 

Loga- 

Numbers. 

rithms. 

Numbers. 

rithms. 

do  =  gravity 

9.  806  m. 

0.  99149 

980.  6  cm. 

2.  99149 

pm  zz  density  of  mercury 

13595.  8 

4.  13340 

13.5958 

1.  13340 

Bu  zz  mere.  col.  for  1  atmos 

0.760 

9.  88081 

76.0 

1.  88081 

pb  zz  density  of  hydrogen 

0.  089996 

8.  95422 

0.  000089996 

5.  95422 

Po  =  Pm  B»  =  Ph  '  (weight) 

10333. 

4.  01421 

1033.  3 

3.  01421 

TJ 

114815. 

5.  05999 

11481500. 

7.  05999 

i  —                (  noiti.  tu  iiios) 
Ph 

jf0  —  temperature 

273. 

2.  43616 

273. 

2.  43616 

I 

Ra  zz  ™   —  gas  constant 
-"o 

420.  56 

2.62383 

42056. 

4.  62383 

v0  zz       zz:  specific  volume 

Ph 

11.  112 

1.  04578 

11112. 

4.  04578 

Po  f'o  =  l 

114815. 

5.  05999 

11481500. 

7.  05999 

^r.=« 

114815. 

5.  05999 

11481500.    i  7.05999 

TABLE  9. —  Transition  to  constants  for  a  solar  hydrogen  atmosphere. 


Formulas. 

M.  K.  S.  system. 

C.  G.  S.  system. 

Loga- 

Loga- 

Numbers. 

rithms. 

Numbers. 

rithms. 

G  =  gig. 

28.  028 

1.  44759 

28.  028 

1.  44759 

Gp0  =  p  (weight) 

289600. 

5.  46180 

28960. 

4.  46180 

i'0  —  v  (same  density) 

11.419 

1.04578 

111112. 

4.  04578 

p  v  —  1 

3218000. 

6.50758 

321800000. 

8.  50758 

G  T0=  T 

7651.6 

3.  88375 

7651.  6 

3.  88375 

Ro  =  R 

420.  56 

2.  62383 

42056. 

4.  62383 

RT=l 

3218000. 

6.  50758 

321800000. 

8.  50758 

26 


TABLE  10. — Fundamental  constants  for  a  hydrogen  atmosphere  on  Hie  sun. 


Data. 

Formula). 

Meter-kilogram-second  . 

Centimeter-gram-second. 

Number. 

Logarithm. 

Number. 

Logarithm. 

Radius  of  the  sun 

r 

694800800  m 

8.  8418603 

694800  80000  cm 

10.  8418603 

Gravity  acceleration  at  the  surface 

g    —Gga  =  28.  028x9-  806 

274.  843 

2.  4390843 

27484.  3 

4.  4390843 

Modulus  of  common  logarithms 

M 

0.  4342945 

9.  6377843—10 

0.  4342945 

9.  6377843—10 

C  Mercury 

Water 
Density      \ 
1  Air 

Pm 
Pi 

Po 

13595.  8 
1000 
1.  29305 

4.  1334048 
3.  0000000 
0.  1116153 

13.  5958 
1.  0000 
0.  00129305 

1.  1334048 
1.0000000 
7.  1116153—10 

I  Hydrogen 

Ph 

0.  089996 

8.  9542232—10 

0.  000089996 

5.  9542232—10 

Height  of  standard  barometer 
Height  of  homogeneous  atmosphere 
Barometric  constant 

Bu  —  P  =  0.  760  X  28.  028 

21.  3013 
3218012 
7409746 

1.3284060 
6.  5075876 
6.  8698033 

2130.  13 
321801200 
740974600 

3.  3284060 
8.  5075876 
8.  8698033 

1        pm  Bu      R  T 

K  —  M  —  Ph  M  —  M 

Pressure  in  units  of  weight 

P 

289608.  1 

5.  4618108 

28960.  81 

4.  4618108 

Pressure  in  units  of  force 

p  J         v_      RT_  K    i     cv 

79596670.  9 

7.  9008951 

795966709 

8.  9008951 

Press,  of  one  terrestrial  atmosphere 
Volume  (specific)  of  hydrogen 

Gas  constant  for  pressure  p 

1 

101323.  5 
11.1116 

420.  565 

5.  0057103 
1.0457768 

2.  6238330 

1013235  dynes 
11111.6 

42056.  5 

6.0057103 
4.  0457768 

4.  6238330 

—    n*   —   ,^    T 

Ptt  * 

Gas  constant  for  pressure  P 

R     —  P"h  9  _  Pm  Bn  9 

1.  15589X105 

5.0629173 

Lifitttyte1 

9.  0629173 

Temperature  at  the  photosphere 
Temperature  gradient 

T  =  28.  028  X  273 
d'f_  A  _  1 

7651.6°  C. 
1.  2563X10-8 

3.  8837546 
2.  0991049—10 

7651.  6°  C. 
1.2563X10-9 

3.  8837546 
1.  0991049—10 

Specific  heat  at  constant  pressure 
Heat  equivalent  of  work 

Coefficient  from  specific  heats 
Ratio  of  the  specific  heats 

cp   =gp^ART 
1                      1 

186503 
0.  00234302 

189261.  5 
1.000005 

5.  2706707 
7.  3697756—10 

5.  2770621 
0.0000021 

18.  99G8 
2.  38G63X10-8 

18926.  15 
1.000052 

1.  2791478 
2.3782527—10 

4.2770621 
0.  0000228 

—  426.  8  a      4.  1855  X  10; 
£             "          9f>    T 

~cv 

The  constants  are  worked  out  for  the  meter-kilogram-second 
(M.  K.  S.)  system  and  for  the  eentimeter-gram-second  (C.  G. 
S.  )  system,  respectively,  the  formulae,  which  are  well  known, 
being  found  in  Table  64  of  the  Report  of  the  Chief  of  the 
Weather  Bureau,  1898-99,  Vol.  II. 

If  hydrogen,  as  a  perfect  gas,  conforms  to  the  Boyle-Gay 
Lussac  law  at  so  high  a  temperature  as  7651.6,  then  there 
must  be  some  stratum  in  the  sun's  atmosphere  where  the 
density  is  the  same  as  it  is  under  the  standard  conditions  on 
the  earth.  If  the  gas  ceases  to  be  perfect  to  some  extent,  this 
statement  must  be  proportionately  modified,  but  in  any  case 
even  approximate  conditions  will  be  very  valuable  as  giving  a 
general  view  of  the  prevailing  state  of  solar  physics,  in  which 
a  footing  of  some  sort  is  a  desideratum  for  meteorology  in 
general.  We  next  determine  the  temperature  gradient  by  the 
computation  in  Table  10,  in  which  the  same  constants  are  em- 
ployed as  above,  except  that  their  values  have  been  determined 
with  greater  precision. 

To  obtain  the  temperature  gradient  per  meter,  or  the  adia- 


in  the  M.  K.  S.  system  must  be  multiplied  by  1000,  and  in  the  C.  G. 
S.  system  it  must  be  multiplied  by  10000  so  that  they  both  give 


:  0.000012563°  C.  per  meter,  or, 


dT 


(79)     —  dh  =  0.012563°  C.  per  1000  meters. 

This  can  be  checked  from  the  terrestrial  adiabatic  rate,  which 
is  9.86938  per  1000  meters,  by  multiplying  by  —  • 

(80) 


dT 
'dh 


^ 

X      sw 


(81) 


0.012563=  9.86938  x  7 


batic  rate  of  fall  of  temperature  per  meter,  the  value  of  — 


— 

dh 


(28.028)a 

The  rate  of  the  fall  in  temperature  in  the  atmosphere  of  the 
sun  is  very  slow  according  to  this  computation,  so  that  varia- 
tion in  the  density  of  the  gases  is  not  due  so  much  to  changes 
in  temperature  as  to  changes  in  pressure,  which  are  very  rapid, 
as  is  shown  in  Table  11  and  fig.  21.  The  approximate  formula 


27 


is  all  that  is  necessary  in  this  discussion  because  of  the  steady 
state  of  the  temperature  just  indicated. 


Let  P0=the  pressure  of  28.028  atmospheres,  where  ha, 
height,  is  assumed  to  be  zero. 

P  =  the  pressure  in  atmospheres  at  the  height  h. 

K  =  7409.746  kilometers,  the  barometric  constant. 
Then  we  shall  have  the  reduction  formula: 

(82)     logp°=;i~\  and    logP  =  log  Pt  -  ~  • 

The  value  of  A  in  seconds  of  arc  is  found  from 

radius  of  sun  in  kilometers 
(  83  )     1  '  (second  of  arc)  = 


the 


of  8un  in  seconds 


694800.800 


16' X  60  =960' 


;  723.751  km. 


DISTRIBUTION  OF  THE  PRESSDKE,  TEMPERATURE,  AND  DENSITY  IN  A  SOLAR 

HYDROGEN  ATMOSPHERE. 

P 

Since  in  a  perfect  gas  Pv  =       =  RT,  we  shall  have  for  the 

f> 

i       •*  P 

density,  p  =  —. 


In  order  to  compute  11,  the  gas  constant, 


we  take  R  =  -— ,  where, 
I'1 

P  =  28.028  atmospheres, 

P  =  0.089996, 

T=  7651.6°,  whence  we  obtain 

R  =  0.040702     [logarithm  =  8. 6096146] . 

The  values  resulting  from  the  computation  are  given  in 
Table  11  and  fig.  21,  "Distribution  of  the  pressure,  tempera- 
ture, and  density  in  a  solar  hydrogen  atmosphere."  The  indi- 
cations regarding  the  prevailing  pressure,  derived  from  the 
behavior  of  certain  lines  in  the  solar  spectrum,  are  that  the 
reversing  layer  is  under  a  pressure  of  about  5  atmospheres,  or 
possibly  as  little  as  3  atmospheres  (Astrophysics,  February, 
1896,  p.  139;  May,  1898,  p.  327;  April,  1900,  p.  240).  Accord- 
ing to  Table  11  the  pressure  at  the  height  8"  above  the  stratum 

TABLE  11. — Distribution  of  the  pressure,  temperature,  and  density  in  the  solar 
hydrogen  atmosphere. 


h"          h 
in  arc.    in  km. 

h 
K 

P 

T 

p 

Height  of  layer 
(A  —  1)"  above  photo- 
sphere. 

45 

32568.  75 

4.  39539 

0.001 

7242.  4 

0.000004 

38 

Top    of    inner 

corona. 

40 

28950.  00 

3.  90702 

0.003 

7287.  9 

0. 

000012 

33 

35 

25331.25 

3.41864 

0.011 

7333.  4 

0 

000036 

28 

30 

21712.50 

2.  93026 

0.033 

7378.  8 

0 

000110 

23 

25 

18093.  75 

2.44189 

0.101 

7424.  3 

0 

000335 

18 

20 

14475.  00 

1.95351 

0.312 

7469.  7 

0. 

001026 

13 

18 

13027.  50 

1.75816 

0.489 

7487.  9 

0 

001605 

11 

16 

11580.  00 

1.56281 

0.767 

7506.  1 

0 

002510 

9 

14 

10132.  50 

1.  36746 

1.203 

7524.  3 

0. 

003927 

7 

Top  of  chromo- 

sphere. 

12 

8685.  00 

1.  17210 

1.886 

7542.  5 

0. 

006143 

5 

10 

7237.  50 

0.  97676 

2.957 

7560.  7 

0 

009609 

3 

9 

6513.  75 

0.  87908 

3.703 

7569.  8 

0. 

012018 

2 

8 

5790.  00 

0.  78140 

4.636 

7578.  9 

0. 

015031 

1 

Reversing 

layer. 

7 

5066.  25 

0.  68380 

5.805 

7587.  9 

0. 

018796 

0 

Top  of  photo- 

sphere. 

6 

4342.  50 

0.  58605 

7.270 

7597.0 

0. 

023512 

—1 

5 

3618.75 

0.  48838 

9.  104 

7606.  1 

0 

029406 

—2 

4 

2895.  00 

0.  39070 

11.400 

7615.2 

0. 

036779 

—3 

3 

2171.25 

0.  29303 

14.275 

7624.  3 

0.  045999 

—4 

2 

1447.  50 

0.  19535 

17.  875 

7633.  4 

0 

057532 

—5 

1 

723.  75 

0.  09768 

22.  383 

7642.  5 

0. 

071955 

—6 

0 

0 

0 

28.  028 

7651.6 

0. 

089998 

—7 

Within    the 

photosphere. 

Fro.  21. — Distribution  of  the  pressure,  temperature,  and  density  in  a 
solar  hydrogen  atmosphere. 

having  a  pressure  of  28.028  atmospheres  is  4.636,  and  this 
may  be  adopted  as  the  height  of  the  reversing  layer.  If  the 
top  of  the  photosphere  is  1"  below  fche  reversing  layer,  the  top 
of  the  chromosphere  5"  above  it,  and  the  top  of  the  inner  corona 
35"  above  the  top  of  the  photosphere,  then  the  layer  at  pres- 
sure 28.028  atmospheres  is  7"  below  the  top  of  the  photosphere, 
and  is  probably  in  the  midst  of  the  photospheric  shell.  The 
temperature  gradient  is  a  straight  line,26  but  the  pressure 
and  density  are  distributed  on  curves  of  the  logarithmic  type. 
From  28  to  5  atmospheres  the  pressure  and  density  change 
very  rapidly,  but  from  2  to  0  atmospheres  they  change  very 
slowly.  There  is  a  quick  transition  in  the  rate  of  change 

dT        1 

26  Since  the  temperature  gradient,  —  -jr-  =  -=- ,  was  computed  for  the 

stratum  within  the  photosphere,  where  P0  =  28.028,  it  follows  that  in  the 
higher  strata,  in  which  P  has  smaller  values  according  to  Table  11,  the 

/     dT\   Pn 

gradient  will  be  greater  in  the  proportion,  I — dh/P'  ass'gning  suc- 
cessive values  to  n  in  the  several  strata.  Hence,  the  temperature  fall  is 

C I dT\  (dT\ 

—  A  Tu= —    I   I  -sir-  I     dh,  where    ITT")     increases  toward  the  top  of 

the  solar  atmosphere.     Computations  for  the  successive  layers  show  that 
the  temperature  fall  is  slow  up  to  the  level  of  P=  1  atmosphere,  beyond 
which  it  increases  very  rapidly  as  the  density  diminishes,  so  that  the 
temperature  of  space  is  reached  at  the  top  of  the  inner  corona. 
We  obtained  the  following  temperatures: 

Initial  stratum  in  photosphere  P=28.028,  Tr=76520 

Top  of  the  photosphere  P=  5.805,7=7500° 

Top  of  the  reversing  layer  P=  4.636,  T=  7450° 

Top  of  the  chromosphere  P=   1.500,7=6950° 

This  law  gives  too  low  temperatures  at  the  top  of  the  inner  corona 
to  be  acceptable  at  present.  Eeferring  to  the  earth's  atmosphere,  the  law 
of  cooling  is  not  the  adiabatic  rate,  but  the  gradient  is  nearly  the  same  as 
that  found  for  the  lower  strata  in  all  levels  up  to  16,000  meters;  that  is  to 
say,  cooling  takes  place  at  a  uniform  rate.  The  law  of  cooling  in  the  solar 
atmosphere  is  a  function  which  is  not  now  known,  and  it  may  fall  be- 
tween the  two  extreme  types  indicated  above.  The  entire  subject  de- 
mands a  careful  research. 


28 


between  5  and  2  atmospheres,  and  in  the  midst  of  this  the 
reversing  layer  and  chromosphere  are  located.  It  is,  there- 
fore, probable  that  the  action  in  the  reversing  layer  which 
sends  forth  visible  light  waves  is  due  to  rapid  transmissions 
in  pressure  and  density,  rather  than  to  any  changes  of  tem- 
perature. This  favors  the  theory  proposed  for  the  explanation 
of  the  reversing  layer  by  Becquerel,  Wood,  and  Julius,  namely, 
that  it  is  due  to  contrasts  of  density,  and  in  accordance  with 
which  the  phenomenon  has  been  reproduced  in  the  laboratory. 
Compare  pages  65  and  162,  Eclipse  Meteorology  and  Allied 
Problems,  Weather  Bureau  Bulletin  I. 

The  shifting  and  the  broadening  of  the  lines  in  the  spectrum 
are  due  to  a  variation  of  pressure  and  density  rather  than  to  a 
change  of  temperature.  It  is  also  seen  that  the  density  of 
the  hydrogen  approaches  zero  at  the  height  of  the  top  of  the 
inner  corona.  The  coincidence  in  the  observed  boundaries 

TABLE  12. — ComptUation  of  the  pressures,  temperatures,  and  densities  at  the 
surface  and  within  the  sun  by  Nipher's  formulae. 

Fundamental  constants. 


of  these  layers  in  the  sun's  atmosphere  with  the  results  of 
this  computation  on  the  physical  state  is  evidently  so  perfect 
as  to  argue  strongly  for  the  correctness  of  the  physical  con- 
stants employed.  The  outcome  goes  to  show  that  the  photo- 
sphere is  the  region  where  great  changes  in  pressure  are 
taking  place,  so  that  violent  circulations,  explosions,  and  chem- 
ical and  electrical  combinations  must  prevail,  and  observations 
show  that  this  is  the  case.  From  the  values  here  employed 
we  can  readily  compute  many  other  important  thermodynamic 
relations. 

It  may  be  observed  that  the  Smithsonian  Astrophysical  Ob- 
servatory computes  from  the  Washington  observations  a  tem- 

TABLE  13. —  Transformation  factor  from  perfect  gases  to  the  material  of  the 
sun  within  the  photosphere. 


Formula  Pl  rz-s 

Ps resurface  pressure  by  Nipher's  formula 
ph  =  density  of  hydrogen  at  surface  of  sun 


Numbers. 
2.9004x10" 
0. 000089996     5.  954223—10 


Logarithms. 

14.  462460 


M 

1 

Numbers. 
=  total  mass  of  the  sun                         2.  0132X1033 

Logarithms. 
33.  303878 

pf  =  surface  density  by  Nipher's  formula 
P2  =  corresponding  pressure  from  inside 

0.  37255 

7.  0065  XlO10 

9.  571182—10 
10.  845501 

T? 

i=  gravitation  constant                           1.  5173X  107 

7.  181073 

P,  :=  pressure  found  from  outside  conditions 

7.  95967  XlO8 

8.  900895 

r 

=:  radius  of  the  sun  in  centimeters  694800  80000. 

10.  841860 

F  —  transformation  factor 

88.  025 

1.  944606 

T 

=:  absolute  temperature  at  surface              7651.  6° 

3.  883755 

.R2=  gas  constant  for  Pfrom  Nipher's  for- 

1.0175X10" 

11.  007523 

Density  at  surface  and  within  the  sun. 

mula 

f 

0.78    M 

Rl  =  gas  constant  for  P  from  hydrogen 

1.  1559X109 

9.  062917 

P 

—  —  i  —  •  -j-  —  surface  density                    0.  37255 

47T            ?"*^ 

9.  571182 

F  :=  transformation  factor 

88.  025 

1.  944606 

r 

—      Pa     1.43287           1]rfn/-Arlnnaii"ir                 037121 

9.  569621 

Some  such  factor  as  88  is  required 

to  change  the  conditions 

~  3.  86  —    3.  86    —  surface  density 

* 

—  average  density  from  astronom-           1.43287 
ical  data 

0.  156208 

outside  the  photosphere  for  perfect 
photosphere  for  nonperfect  gases  or 

gases  to  those  inside  the 
liquids. 

*•. 

=  0.  545  r  =  distance  of  stratum  pa      3.  7867X  10'° 

10.  578257 

TABLE  14.  —  Specific  heats  c  ,  c,,  quantity  of  heat  Q,  and  work  W,  in  tlte 

from  center 

surface  stratum  of  the  sun. 

• 

—  —  rzspeciflcvolumeatthesurface             2.  6842 

0.428818 

i           K          3n  —  4 

Numbers. 
3c 

Logarithms. 

Pressure  at  the  surface  and  within  the  sun. 

ep             \—  K—  1  —  2  —  2n 
(  =  assumed  value 

.  D 

3.4615 

0.  539264 

0.  636    M  2A? 

1 

P 

14.  462460 

A               =  heat  equivalent  of  work 

9   ^789^^      1  O 

~  —  o  —  •  —  —  j—  zi:  surface  pressure       2.  9004  XlO14 

4.1855X10' 

pa 

—  5.  40  P  z=  average  pressure                1.  5662x  1015 

15.  194854 

R              =  gas  constant 

1.0175X1011 

11.  007523 

r. 

=  0.  502  r  =.  distance  of  stratum  Pa      3.  4879X  1010 

10.  542564 

AR           — 

2431.  0 

3.  385776 

from  center 

3w  —  4 

i  j-»                                     Or       4   T~* 

R  T  at  the  surface  of  the  sun. 

cf                —  AR  2  _  27i  -:  3-  5  AR 

8414.  8 

3.  925040 

l 

Mk* 

Assume  3.  4615  AR 

=  0.818-^-                                              7.8103X10" 

14.  892668 

2cp 

16829.  6 

RT 

3AR 

7293.  0 

=  Pu     (The  coefficient  should  be      7.7854x10" 

14.  891278 

more  fully  developed) 

±AR 

9724.  0 

R 

Pi) 

—  -y  —  the  gas  constant                       1.0175x10" 

11.007523 

/dQ\       _                           specific  heatdue 
~  \d  T/  n  —       (  f  "i"                 to  contraction 

18138.8 

4.  258609 

Temperature  at  the  surface  and  within  the  sun. 

n                -     (\      |  '  Q  A  j3   —  A*  -L  ciosGiy 

1.1008 

0.  041699 

T 

—  273X28.028                                              7651.6° 

3.  883755 

p"r 

T. 

=.  1.  08  T                                                        8263.  8° 

3.917179 

c                -  W~  £y+SXR 

0.7519 

9.  876184 

rt 

=  0.707r                                                  4.9122X1010 

10.  691279 

—  0.  75  closely 

—  A  T=  8263.  8°  —  7651.  6°  =  612.  2°                       612.  2° 

2.  786893 

+  Ar 

—  1.000  r  —  0.707  r  =  0293  r  in  km.            203577. 

5.  308728 

TB-                   i  CQA  M^     work  of  compres- 

1.2225X1048 

48.  087250 

2r    -     sion 

AT1 

_  —  —  temperature  gradient  within  the        0.0030072 

7.  478165—10 

Q              ~  0.7519  W  =  heat  radiated 

0.  9192X1048 

47.  963434 

sun  per  1000  meters 

TT  —  Q     rr  excess  of  work  energy  over 

0.3033  XlO48 

47.  481872 

Mass  of  the  sun. 

heat  energy 

I 
M    • 

ZRTr 

33.  302991 

Q 

3.03 

0.  481562 

•  =  1.22  —  IT,  —  rzmass                              2.  0091X1033 

W—Q 

W 

4riq 

;  —  Adopted  value  from  Newcomb          2.  0132X1033 

33.  303878 

W-Q 

.  Uo 

Weight  of  1  gram  at  the  surface  of  the  sun. 

(8_5n)(4-3n) 

7077   9 

3 

o  p  m            7.2 

c'                  -cf     3  (2  —  n)2(5«  —  3)'  ' 

(  p  '  (  (  .  £t 

' 

—  f\/  A          _  _  IV 

4.  438178 

—  cp  —  0.180  AR 

9 

*•               r 
=  980.  6  X  28.  028                                            27484. 

4.  439084 

cf      8414.  8 

1.  0548 

0.  023190 

-  cv  —  7977.  2 

29 


perature  of  about  6000°  for  the  atmosphere  of  the  sun,  although 
it  is  quite  certain  that  a  higher  station,  as  Mount  Whitney, 
would  give  a  greater  temperature,  say  6500°.  This,  of  course, 
takes  account  of  the  absorption  in  the  earth's  atmosphere,  but 
not  of  that  in  the  sun's  atmosphere.  It  seems  probable  that 
the  equivalent  of  1000°  C.  may  be  absorbed  from  the  stratum 
included  between  the  midst  of  the  photosphere  and  the  top 
of  the  inner  corona.  If  this  is  not  the  case,  then  the  outgoing 
radiation  of  the  sun  must  be  such  as  to  give  nearly  4.0  gram- 
calories  per  square  centimeter  per  minute  on  the  outer  surface 
of  the  atmosphere  of  the  earth.  The  relative  absorption  in 
the  atmospheres  of  the  sun  and  the  earth,  respectively,  will 
be  much  more  readily  determined  if  it  can  be  admitted  that 
the  temperature  of  the  sun  about  7"  within  the  photosphere 
is  approximately  7652°.  In  the  following  discussion  the  sur- 
face stratum  is  that  which  is  7"  below  the  visible  boundary  of 
the  photosphere,  where  the  pressure  is  taken  as  28.028  at- 
mospheres. The  various  comments  made  by  Buckingham  and 
Day  as  to  the  value  of  temperatures  extrapolated  from  ter- 
restrial to  solar  conditions  have  their  importance,  but  it  is 
believed  that  we  shall  be  able  to  gain  a  footing  by  other 
processes,  such  as  thermodynamic  relations,  and  thereby  de- 
termine the  thermal  condition  of  the  sun  without  such  an 
overstepping  of  the  limits  of  the  actual  practicable  experi- 
ments of  the  laboratory.  We  will  proceed,  in  Tables  12  to  14, 
to  consider  the  conditions  within  the  solar  mass,  with  the  aid 
of  Nipher's  formulae,  and  to  show  that  here,  too,  there  is  ground 
for  encouragement,  because  of  the  numerous  agreements  be- 
tween two  independent  sets  of  data,  namely,  the  astronomical 
quantities  and  the  thermodynamic  values. 

DISCUSSION    OF    THE    VALUES    DERIVED    FKOM    TABLES    12    TO    14. 

Table  12,  "  Computation  of  the  pressures,  temperatures,  and 
densities  at  the  surface  and  within  tke  sun  by  Nipher's  for- 
mulae," contains  a  series  of  values  at  the  surface  stratum  in 
the  photosphere,  where  the  pressure  has  been  taken  at  28.028 
atmospheres  as  the  result  of  external  conditions.  These  have 
now  been  computed  from  astronomical  data  M,  k*,  r,  and  the 
assumed  temperature  7G51.6.  The  purpose  is  to  compare  these 
two  sets  of  values,  one  computed  from  external  conditions,  and 
the  other  from  the  internal  conditions,  the  former  for  strictly 
perfect  gases,  as  hydrogen,  and  the  latter  from  such  non-per- 
fect gases  or  liquid  material  as  makes  up  the  body  of  the 
sun.  While  the  law  Pu  =  RT  applies  to  perfect  gases,  we  may 
yet  obtain  some  approximate  idea  of  the  state  of  the  sun  in- 
side the  photosphere  if  a  transformation  factor  can  be  found 
by  which  to  pass  from  the  first  system  to  the  second.  In  a 
circulating  mass  like  the  sun  it  is  probable  that  something 
like  this  law  applies  throughout  the  mass.  At  any  rate  the 
view  can  be  tested  to  some  extent  by  studying  the  two  sets  of 
data.  There  is,  of  course,  some  danger  of  arguing  in  a  circle 
through  so  complex  a  system  of  formulae,  but  I  think  that  the 
general  conditions  herein  exhibited  conform  more  closely  to  a 
natural  solar  mass  than  the  results  heretofore  derived  by  the 
use  of  Eitter's  formulae. 

The  density. 

The  average  density  of  the  sun  from  astronomical  data  is 
1.43287,  and  it  is  a  denser  liquid  than  water.  The  surface 
density  is  0.37255,  or  about  one-fourth  the  average  density. 
This  latter  occurs  at  the  distance  0.545?-  from  the  center  of  the 
sun,  and  if  anything  like  the  same  gradient  of  density  is  main- 
tained throughout,  the  density  near  the  center  of  the  sun  is 
not  far  from  5.7,  which  is  about  the  mean  density  of  the  earth. 
We  may,  therefore,  assign  a  more  or  less  solid  nucleus  to  the 
sun,  which  becomes  viscous  at  a  distance  of  about  one-third 
the  radius  from  the  center,  and  soon  thereafter  mobile.  The 
transitions  within  the  aun  are  gradual,  but  at  the  photosphere 
there  is  apparently  a  mixture  of  liquid  and  gaseous  masses  in 
active  transitions,  and  these  seem  to  be  the  conditions  indi- 


cated by  the  phenomena  observed  in  the  sun  spots.  The 
prominences,  faculse,  and  chromosphere  are  strictly  in  a 
gaseous  atmosphere;  the  photosphere  is  a  mixture  of  gases 
and  liquids,  and  the  interior  consists  of  a  circulating  liquid 
passing  into  a  solid  nucleus  near  the  center.  While  the  sun's 
pressure  by  gravitation  alone  would  increase  the  density  of  its 
constituents,  the  temperature  is  at  the  same  time  high  enough 
to  balance  this  tendency  to  compression,  so  that  the  material  in 
the  sun  is  in  about  the  same  state  as  the  material  of  the  earth, 
except  that  here  the  outer  layers  have  advanced  toward  solidi- 
fication under  the  prevailing  low  temperature.  A  contracting  . 
sun,  in  order  to  keep  up  its  radiation,  must  be  circulating 
freely,  and  this  precludes  a  very  high  degree  of  viscosity,  ex- 
cept near  the  center. 

The  pressure. 

Beginning  with  a  pressure  of  28.028  atmospheres  in  that 
layer  of  the  photosphere  where  the  temperature  is  7652°, 
which  on  the  sun  is  equivalent  to  7.96  x  10s  dynes,  we  compute 
that  for  a  hydrogen  gaseous  envelope  the  pressure  practically 
vanishes  at  the  top  of  the  inner  corona.  Beyond  this  layer, 
into  which  hydrogen  is  ejected  in  the  prominences,  the  condi- 
tions are  favorable  for  all  the  electrical  and  magnetic  phe- 
nomena belonging  to  the  cathode  rays  in  rarefied  gases.  At 
the  photosphere,  where  the  materials  change  from  gases  to 
vapors  and  liquids,  there  is  a  corresponding  equivalent  increase 
in  pressure  up  to  2.90  x  10'4  dynes.  It  would  take  this  increase 
in  pressure  to  pass  from  the  gaseous  to  the  fluid  state  at  the 
high  temperature  there  prevailing.  If  a  fluid  may  be  consid- 
ered as  a  gas  brought  by  pressure  at  a  given  temperature  to 
the  liquid  condition,  then  this  pressure  difference  also  repre- 
sents the  explosive  energy  when  the  liquid  changes  to  a  gas. 
If  the  liquid  is  elevated  from  the  interior  to  the  surface  of  the 
sun  by  convection  currents,  then,  on  reaching  the  surface,  it  may 
greatly  expand  and  even  explode  when  vaporization  takes  place, 
as  is  commonly  observed  on  the  edge  of  the  sun  through  the 
enormous  velocities  measured  by  the  change  in  wave  lengths,  by 
the  Doeppler  principle,  or  by  anomalous  dispersion.  Within 
the  body  of  the  sun,  at  the  distance  0.5  radius  from  the  center, 
the  pressure  is  1.57x  1015  dynes,  which  is  5.4  times  as  much  as 
at  the  surface.  By  the  same  ratio,  the  pressure  would  be  eleven 
times  as  much  at  the  center,  though  this  law  doubtless  changes 
within  the  nucleus.  The  pressure  is  comparatively  uniform 
below  the  sun's  surface,  and  widely  discontinuous  at  the  sur- 
face. Hence,  the  convectional  currents  and  the  dependent 
phenomenon  of  rotation  in  latitude  are  leisurely  motions  com- 
pared with  the  explosive  action  at  the  surface  layers. 

The  temperature  and  the  gas  constant. 

Nipher's  coefficients  are  carried  to  only  three  decimals,  which 
is  doubtless  sufficiently  accurate  for  the  determination  of  the 
value  of  the  contractional  constant  n.  It  is  not  quite  suffi- 
ciently accurate,  however,  to  give  proper  check  values  from 
one  formula  to  another,  but  I  have  not  thought  it  worth  while 
to  carry  this  computation  beyond  the  approximate  stage.  If  we 
pass  from  a  perfect  gas  to  a  fluid,  the  value  of  the  gas  constant 
adopted  must  be  interpreted  as  merely  suggesting  important  re- 
lations, and  too  much  emphasis  must  not  be  laid  upon  certain 
obvious  criticisms  which  naturally  arise.  We  may  suppose  that 
the  mass  of  the  sun  beneath  the  photosphere,  while  apparently 
fluid  or  viscous,  yet  moves  in  accordance  with  the  general  law, 
by  reason  of  convection,  so  that  it  is  continually  readjusting 
itself  to  conform  somewhat  closely  to  this  general  law  of 
gaseous  elasticity.  At  any  rate,  this  is  the  theory  upon  which 
we  have  proceeded  in  the  discussion.  We  compute  the  product 

p 
E  Tbj  Nipher's  formula,  and  check  it  with  the  product  —  found 

from  the  pressure  and  density,  and  then  with  the  temperature 
T  =  7651.6°  find  K  =  1.0175  x  10"  for  the  fluid  of  density 
0.37255  in  the  surface  layer.  The  temperature  within  the  sun 


30 


at  the  distance  0.707  radius  from  the  surface  becomes  8264°, 
and  at  this  rate,  an  increase  of  612°  in  0.293  radius,  the  total 
increase  from  the  surface  to  the  center  is  2089°,  making  the 
central  temperature  9741°.  This  gives  an  average  gradient 
of  — 0.0030072°  per  1000  meters  from  the  center  to  the  surface. 
We  find,  also,  the  gradient  from  the  photosphere  to  the  top  of 
the  inner  corona  to  be  — 0.012563°  per  1000  meters.  The  gra- 
dient of  the  temperature  is  about  four  times  as  great  in  the  at- 
mosphere of  the  sun  as  inside  the  photosphere.  The  cooling  is, 
therefore,  more  rapid  outside  than  it  is  inside  the  photosphere. 

'  The  mass  of  sun,  the  weight  of  1  gram  on  the  surface  of  the  sun, 
and  the  transformation  factor. 

The  mass  of  the  sun  is  2.0091  x  1033  by  Nipher's  formula, 
agreeing  closely  with  that  adopted  from  Newcomb,  2.0132  x  10SS, 
the  former  being  computed  through  the  product  RT,  and  thus 
checking  all  the  quantities.  The  weight  of  1  gram  at  the  sur- 
face of  the  sun  is  27428  by  Nipher's  formula,  through  the 
product  RT,  and  this  agrees  with  the  simple  product  g  = 
980.6x28.028  =  27484,  thus  checking  again.  The  transition 
factor  from  a  perfect  gaseous  system  to  that  actually  existing 
at  the  surface,  where  the  density  is  0.37255,  is  found  as  indi- 
cated. We  find  the  pressure  corresponding  to  0.37255  instead 
of  that  for  which  the  computation  was  made  in  a  hydrogen 
atmosphere  of  density  0.000089996,  and  obtain  Pt  =  7.0065  x  10'° 
through  Nipher's  formula,  as  if  the  atmosphere  were  of  the 
greater  density.  For  the  actual  hydrogen  atmosphere  we  com- 
puted (Table  13)  Pl  =  7.95967 x  10".  Hence,  Pt  =  88.025  Pv 
so  that  88.025  is  the  required  factor.  Similarly,  the  gas  con- 
stant from  Nipher's  formula  is  R3  =  1.0175  x  10".  It  was  com- 
puted for  the  actual  hydrogen  atmosphere  (Table  13)  to  be 
R1  =  1.1559x10'.  Again,  R3  =  88.025  «,,  so  that  there  is 
mutual  agreement.  Some  such  factor  as  88  is  required  to  pass 
from  the  law  for  perfect  gases,  Pl  v  =  ^  T,  to  that  for  solar 
liquids,  P2  v  =  Mt  T. 

It  will  not  be  advantageous  to  speculate  as  to  what  this  factor 
88  signifies,  but  it  is  not  so  large  as  to  be  improbable  in  passing 
from  a  gaseous  to  a  fluid  state,  as  it  may  stand  for  the  internal 


forces  of  viscosity  or  friction  and  molecular  cohesion,  and  pos- 
sibly for  some  unknown  forces  of  electricity  and  magnetism. 

Specific  heats,  energy  of  radiation,  and  contraction. 

Carrying  the  values  of  the  several  quantities  through  the 
various  formuL-e  we  find  that  they  conform  to  the  prescribed 
conditions,  as  follows: 


Specific  heat  of  contraction  — 

Exponent  and  coefficient 
Heat  energy  of  radiation 
Work  energy  of  contraction 
heat  radiated 


• 
n 

Q 
w 


Ratio 


Ratio 


Ratio 


work  of  gravitation 
heat  radiated 

excess 
work  of  compression 


w 

Q 

W—  Q 
W 


excess  "    W —  Q 

Specific  heat  at  constant  pressure     cp 
Specific  heat  at  constant  volume        <?„ 

cp  ratio  of  the  specific  heats 
*  =  cv  at  the  temperature  7652° 


=  18138.8 

=  1.1  closely. 

=        0.9192  x  1048 

1.2225  x  1048 

=         0.75  closely. 
=         3.00  closely. 

4.00  closely. 

=  8414.8 

=  7977.2 

1.0548 


We  note  that  this  ratio  *  =-'*-=  1.4065   in   terrestrial  condi- 

c» 

tions;  in  solar  conditions  inside  the  photosphere  «=  1.0548; 
and  in  the  hydrogen  envelope  K  =  1.000052  according  to  the 
preceding  discussion. 

Surveying  this  set  of  interrelated  thermodynamic  values, 
and  especially  in  view  of  the  fact  that  they  seem  to  conform 
so  well  with  the.  known  astrophysical  conditions  derived  from 
observation,  and  with  the  astronomical  data  obtained  by  the 
general  laws  of  motion,  we  conclude  that  they  afford  ground 
for  further  research.  If  they  form  the  approximate  basis  for 
a  sound  solar  physics  they  will  become  important  in  further 
meteorological  studies. 


XXXII—  47, 


Chart  XII  A.  Average  monthly  vectors  of  the  general  circulation  in  the  West  Indies  at  the  various  cloud 

levels.    First  arrangement. 


Fi&.ZZ. 


Cuba. 


x=<52°2/i 


<7    F  Jtf  ^4.    JtfJJASOWD 


TX-.  v  r 

Jltntftfton,  tsacmocccez. 


<7 


A    Af 


SO 


c/. 


C/.  Cu. 


^» 


C/. 


C/.  ff. 


Of.  Cv. 


N> 


r-^ 


A.Sf. 


*t=-> 


7 


A.Ou. 


7r~7 


1*r- 


Cts. 


3. 


Wtnct 


XXXII— 48. 


Chart  Xn  B.  Average  monthly  vectors  of  the  general  circulation  in  the  West  Indies  at  the  various  cloud 

levels.    First  arrangement. 


2*1(7.26'.          Sctrtto  jDomingo. 


Fig.  27. 


,  Porto  Rico  . 


<7    F  Jif  ^4 


A    SO 


<f     f 


M   J 


S     0     JV    2) 


c/. 


/.  61. 


^* 


Ci.  Cu. 


A 


A 


A.Cts. 


<<* •£<<<• 


^^ 


S.Cu. 


\ 


£V, 


Cu. 


f^ 


s. 


S. 


.. i. :l 


I      ,', 


Wtrrd 


.  J&oseau,,  Dominica.  •K=.6'J°23' 


Ci.-Ctr. 


A.Sf. 


A.Cu. 


S.Cu. 


On. 


*= 


C/:  Cu. 


?' 


d.Cis. 


s. 


Wtrref 


<t 


71 


~7 


^=f^= 


fc^ 


7 — 1 


of  Ve/o<Sity 


XXXII— 49. 


Chart  "En  o.  Average  monthly  vectors  of  the  general  circulation  in  the  West  Indies  at  the  various  cloud 

levels.    First  arrangement. 


Fig.  3O.  Bridgetown,  Barbados. 


69*37' 


Ficf.SJ.    Willemstad.,  dtracao.  &9°  o 


<7    f  Af  jl    Af 


A    &    O 


Af   «/     J    A     £      O     XT    J) 


c/: 


c/. 


C/.Q. 


=*^» 


C/.  Ces. 


A.&. 


A  C 


A.Cu. 


J.Cu. 


S.Cu. 


C 


<$. 


e? 


t —  ^ 


&-  32.  for-t  ofsSjya.in, 


0 


o/.  a. 


j— • t 


*^~* 


, 


st.Sf. 


A.Cts. 


S.Cu. 


V    ^ 


Cu. 


,/^ 


XXXII— 50. 

Chart  TETTT  A.  Average  monthly  vectors  of  the  general  circulation  in  the  West  Indies  at  the  various  cloud 

levels.    Second  arrangement. 


XXXII— 51. 


Chart  "xrn  B.  Average  monthly  vectors  of  the  general  circulation  in  the  West  Indies  at  the  various  cloud 

levels.    Second  arrangement. 


XXXII— 52. 

Chart  Xm  0.  Average  monthly  vectors  of  the  general  circulation  in  the  West  Indies  at  the  various  Cloud 

levels.    Second  arrangement. 


.A.  St.  arrcf  C/.  Cu.    afiou/d  be  trorrrspoti  of 


j 

<0 


i 


T 


i 


i 


K 


\ 


i 


\ 


i 


1 


i 


» 


\ 


\ 


0 


t 


V 

1 


> . 


1 


at 

I 


I 

•s 

to 
<D 

'•5 


I 
I 


VA 


\ 


J 


2 


\ 


\ 


\ 


\ 


\ 
\ 


\ 


\ 


T 


(B  ^} 

8» 

o 


O 

CD 
J-. 


¥ 


t 


t 


\ 


1 


\ 


J 


\ 


\ 


m 
o 

I 


\ 


\ 


i 


\ 


\ 


1 


\ 


\ 


\ 


\ 


\ 


\ 


\ 


V.— RESULTS  OF  THE  NEPHUSCOPE  OBSERVATIONS  IN  THE  WEST  INDIES  DURING  THE  YEARS  1899-1903. 


METHODS    OF    OBSERVATION    AND    REDUCTION. 

The  observers  of  the  United  States  Weather  Bureau  occu- 
pied eleven  stations  in  the  West  Indies  during  the  years  1899- 
1903,  and  the  opportunity  was  utilized  to  make  a  survey  of  the 
motions  of  the  atmosphere  in  that  region  of  the  Tropics  by 
means  of  nephoscopes. 

The  instruments  were  of  the  Marvin  pattern,  and  the  method 
of  observation,  to  obtain  the  azimuth  and  velocity  of  motion, 
was  identical  with  that  described  in  the  Report  of  the  Chief  of 
the  Weather  Bureau,  1898-99,  Vol.  II,  chapter  2.  The  reduc- 
tions were,  however,  carried  out  more  perfectly  than  in  any 
previous  research  of  the  kind  in  the  following  manner:  (1) 
The  three  readings  at  each  observation  were  reduced  to  a  mean 
azimuth  and  velocity,  for  entry  on  the  computing  sheets.  (2) 
Each  vector  V,  <p  was  separated  into  its  rectangular  compon- 
ents, +  S,  +  E,  where  S  is  positive  southward  on  the  meridian, 
and  E  is  positive  eastward  on  the  parallel  of  latitude.  (3) 
The  algebraic  sum  of  each  set  of  components  was  then  taken 
from  month  to  month,  and  the  groups  for  corresponding 
months  during  the  years  1899-1903  combined.  (4)  These  sums 
were  divided  by  the  number  of  observations,  to  obtain  the 
mean  velocity  component  per  observation.  The  observations 
were  taken  for  two  years  in  the  afternoon  hours,  and  for  the 
other  two  years  in  the  forenoon  hours,  so  that  the  diurnal 
variation  was  practically  eliminated  by  putting  the  entire  data 
for  each  of  the  twelve  months  in  a  single  summation.  (5) 
These  mean  ordinates  were  plotted  month  by  month  for  the 
nine  cloud  levels,  and  average  curves  were  drawn  through 
them.  In  spite  of  the  fact  that  the  number  of  observations  is 
large,  when  taken  as  a  whole,  yet,  when  subdivided  among  so 
many  strata,  there  is  more  scattering  of  the  ordiuate  points  in 
certain  levels  than  is  desirable.  The  average  curves  approxi- 
mate the  normal  components  which  would  be  derived  from  a 
very  much  more  extensive  series  of  observations.  The  full 
report  will  contain  the  observed  ordinates  and  those  obtained 
by  graphical  adjustment.  (6)  The  resultant  polar  coordinates 
V,  y  were  then  computed  from  the  rectangular  coordinates. 
Up  to  this  point  the  numerical  data  had  been  carried  forward 
in  the  number  of  millimeters  passed  over  in  twenty-five  sec- 
onds on  the  scale  of  the  nephoscope.  (7)  These  numbers  were 
now  reduced  to  velocities  in  meters  per  second,  by  multiply- 
ing them  by  the  factor  J  H,  where  H  is  the  adopted  height  of 
the  cloud  stratum.  The  values  of  H  were  adopted  from  the 
Washington  cloud  heights,  after  considering  the  heights  ob- 
tained at  Manila  during  the  same  cloud  year,  1896-97.  These 
velocities  and  azimuths  were  transferred  to  charts  drawn  to 
the  scale  1  millimeter  =  1  meter  per  second.  In  preparing 
these  charts  for  publication  in  the  MONTHLY  WEATHER  REVIEW, 
the  original  scale  has  been  reduced  to  0.6  millimeter  =  1  meter 
per  second,  as  shown  by  the  "  velocity  scale  in  meters  per 
second  "  at  the  bottom  of  each  chart  of  the  sets  Chart  XII  and 
XIII,  the  scale  of  Chart  XIV  being  unchanged. 

CHARTS    OF     THE     RESULTING     VELOCITIES    AND    DIRECTIONS     OF     MOTION 
FOR    THE    WEST    INDIES. 

The  vectors  V,  <p  have  been  plotted  for  each  station,  so  that 
the  mutual  relations  of  the  resulting  motions  can  be  properly 
compared  and  studied.  There  are  several  remarks  to  be  made 
about  the  observations  themselves.  At  Willemstad  the  observers 
have  frequently  misnamed  the  cumulus  clouds  as  cumulo-stratus. 
This  becomes  apparent  on  plotting  the  vectors.  The  angles  are 
correct,  but  the  length  of  the  arrows  is  too  great.  I  have  ac- 
cordingly interpreted  the  values  of  7",  and  V  under  strato-cu- 
mulus  as  belonging  to  the  cumulus  level,  and  have  used  the 
reduction  factor  0.5  instead  of  0.9  in  drawing  the  charts. 

At  Bridgetown  the  vector  systems  of  the  alto-stratus  and 


the  cirro-cumulus  levels  have  apparently  been  interchanged. 
As  they  now  stand  at  Bridgetown  they  are  inconsistent  with 
the  flow  of  air  as  determined  at  Basseterre,  Roseau,  Port  of 
Spain,  and  Willemstad;  but  if  they  are  transposed,  then  there 
is  harmony.  The  observation  sheets  indicate  that  the  ob- 
servers have  an  unusually  large  number  of  cirro-cumulus  en- 
tries and  comparatively  few  alto-stratus,  so  that  apparently 
they  were  accustomed  to  name  many  alto-stratus  clouds  as 
cirro-cumulus  clouds.  It  is  not  easy  to  secure  identical  esti- 
mates of  cloud  forms  at  so  many  independent  stations  as  we 
have  used,  and  these  few  instances  of  apparent  discrepancies 
are  gratifying  evidence  of  the  general  excellence  of  the  results 
in  other  respects. 

On  comparing  the  charts  here  presented  with  those  pub- 
lished by  Prof.  H.  H.  Hildebrandsson  for  the  international 
committee,  it  appears  that  he  has  computed  only  the  angle  of 
the  azimuth  of  motion  without  the  velocity,  and  that  the  same 
schematic  velocity  is  entered  throughout  the  year.  Apparently 
the  actual  velocities  have  not  been  computed  for  that  report 
at  any  station.  The  importance  of  having  the  velocity  as  well 
as  the  direction  of  motion  is  evident,  and  this  is  emphasized 
by  examining  the  great  variations  between  the  summer  and 
the  winter  velocities  and  between  those  at  the  different  cloud 
levels  of  each  .station  of  the  West  Indies.  Comparing  the 
Hildebrandsson  and  the  Bigelow  results  for  Havana,  Plate 
VII,  International  Report,  with  fig.  22,  Chart  XII  A,  the  azi- 
muth directions  are  not  in  agreement  in  the  autumn;  com- 
paring those  for  the  Antilles,  Plate  III,  International  Report, 
with  figs.  28,  29,  30,  Charts  XII B,  and  XII C,  Basseterre, 
Roseau,  and  Bridgetown,  the  legend  "Nuages  superieurs" 
should  apparently  be  changed  to  "Nuages  intermediaries"  or 
"Nuages  inferieurs." 

The  vectors  of  the  West  Indian  stations  have  been  plotted 
in  three  forms:  The  first,  Charts  XII  A,  XII  B,  XII  C,  figs.  22 
to  32,  wherein  the  vectors  of  the  same  month  throughout  the 
nine  levels  terminate  on  the  same  vertical  line;  the  second, 
Charts  XIII  A,  XIII  B,  XIII  C,  figs,  33  to  43,  wherein  the  vec- 
tors for  June  terminate  on  the  same  vertical  line  and  the 
others  in  succession,  so  as  to  form  a  continuous  broken  line;  the 
third,  Charts  XIV  A,  XIV  B,  XIV  C,  figs.  44  to  61,  showing  ap- 
proximate normal  vectors  for  winter  and  summer.  The  first 
enables  us  to  study  the  movements  simultaneously  occurring 
in  a  given  month  from  the  surface  wind  to  the  cirrus  level,  and 
from  this  many  important  conclusions  can  be  drawn.  The 
second  makes  more  distinct  the  general  course  of  the  move- 
ment in  the  several  strata  throughout  the  year,  and  especially 
the  nature  of  the  currents  that  depend  upon  the  forces 
producing  the  westward  drift  of  the  lower  levels  and  the 
eastward  drift  of  the  upper  levels,  together  with  the  tran- 
sition levels  between  them.  The  third  system  of  charts 
is  a  composite  of  the  mean  winter  and  the  mean  summer 
systems,  respectively,  some  of  the  minor  irregularities  being 
rectified  in  the  adopted  vectors.  January  and  February  con- 
stitute the  middle  of  the  winter  group,  while  July  and  Au- 
gust are  at  the  middle  of  the  summer  group.  In  adopting 
these  vectors  regard  was  had  to  the  most  probable  balanced 
system  which  is  indicated  by  the  entire  set  of  vectors.  If  the 
reader  has  doubts  as  to  the  accuracy  of  these  final  results,  the 
original  material  of  the  third  set  of  charts  is  to  be  found  in 
the  first  and  second  sets,  or  in  tables  from  which  all  the  charts 
have  been  plotted,  which  will  appear  in  the  full  report.  Nu- 
merous studies  in  the  dynamic  meteorology  of  the  Tropics 
are  how  practicably,  for  the  first  time,  but  as  it  will  require 
much  careful  labor  to  execute  them,  only  some  general  re- 
marks are  required  in  this  place. 

31 


32 


THE  ARCH  SPANNING  THE  TROPICS,  WHICH  DIVIDES  THE  EASTWARD  DEIFT 
FBOM  THE  WESTWARD  DRIFT  OF  THE  GENERAL  CIRCULATION. 

The  general  theory  of  the  circulation  of  the  atmosphere 
shows  that  in  the  temperate  zones  of  the  Northern  and  the 
Southern  hemispheres  there  is  a  strong  prevailing  eastward  com- 
ponent producing  an  eastward  drift,  while  in  the  Tropics  there 
is  a  prevailing  westward  component  causing  a  westward  drift. 
The  tropical  westward  drift  is,  however,  limited  in  altitude,  and 
at  a  certain  elevation  the  drift  reverses  from  a  westward  to  an 
eastward  direction.  The  position  of  the  curve  which  separates 
the  eastward  from  the  westward  drift  varies  with  the  season  of 
the  year.  When  the  sun  is  far  to  the  south  and  the  northern 
winter  prevails,  the  arched  curve  must  be  skewed  to  the  south, 
and  when  the  sun  is  far  to  the  north  and  the  northern  sum- 
mer prevails  the  arch  is  skewed  toward  the  north.  This  is 
on  the  assumption  that  the  foot  of  the  arch  rests  on  nearly  the 
same  latitude  in  winter  and  summer  at  any  given  region  of 
the  earth.  The  high  pressure  belt,  which  fixes  the  position 
of  the  arch  on  the  surface  of  the  earth,  for  the  eastern  portion 
of  the  United  States  lies  somewhere  between  +30°  and  +35° 
north  latitude,  and  crosses  the  Atlantic  coast  at  about  Florida 
and  South  Carolina.  It  is  desirable  to  determine  from  our  ob- 
servations its  exact  location,  but  as  this  is  of  subordinate  im- 
portance for  our  immediate  purpose  it  can  be  passed  over  in 
this  connection.  Further  accounts  of  the  mathematical  sig- 
nificance of  the  tropical  discontinuous  surface  between  the 
prevailing  eastward  and  westward  drifts  may  be  found  by 
consulting  the  full  report,  and  my  paper  in  the  MONTHLY 
WEATHER  REVIEW,  January,  1904,  Vol.  XXXII,  p.  15. 

One  special  purpose  of  the  West  Indian  nephoscope  survey 
for  1899-1903  was  to  determine  this  surface  of  separation  in 
the  higher  levels,  and  its  variation  with  the  season  of  the  year. 
The  velocities  and  direction  of  motion  on  either  side  of  it,  and 
the  numerous  meteorological  inferences  that  can  be  drawn 
from  these  conditions  made  the  work  of  primary  importance 
in  the  development  of  the  dynamics  of  the  atmosphere.  The 
series  of  Charts,  XII A  to  XIV  C,  figs.  22  to  61,  are  now  avail- 
able for  this  purpose.  The  twelve  months,  as  observed,  may 
be  taken  in  two  groups,  of  which  the  winter  group  is  dis- 
tributed about  January  and  February  as  the  central  months, 
and  the  summer  group  about  July  and  August.  If  there  had 
been  simultaneous  observations  in  the  Southern  Hemisphere 
at  latitudes  corresponding  to  those  that  were  occupied  by  the 
West  Indian  stations  in  the  Northern  Hemisphere,  we  should 
then  have  the  data  applying  simultaneously  to  the  entire  tropic 
zone.  The  same  result  can  be  closely  approximated  by  treating 
the  winter  group  as  representing  the  north  tropical  zone,  and 
the  summer  group  as  representing  the  south  tropical  zone, 
during  the  northern  winter.  Hence,  by  using  the  results  from 
November  to  April  in  the  northern  latitudes,  and  assuming 
that  during  this  period  the  conditions  observed  for  the  north- 
ern latitudes  during  May  to  October  then  prevailed  in  the 
southern  latitudes,  the  synchronous  action  of  the  circulation 
can  be  found  for  the  northern  winter  throughout  the  Tropics. 
By  reversing  this  process  the  corresponding  results  for  the 
northern  summer  are  obtained. 

An  inspection  of  the  vectors  of  motion  in  the  winter  months 
shows  that  for  Havana,  Cienfuegos,  and  Santiago,  Cuba,  with 
mean  latitude  22°,  the  reversal  is  about  midway  between  the 
cumulo-stratus  and  alto-cumulus  levels,  or  at  approximately 
3500  meters  above  the  sea  level.  At  Kingston,  Santo  Domingo, 
San  Juan,  Basseterre,  Roseau,  and  Bridgetown,  having  the 
mean  latitude  of  17°,  the  reversal  is  apparently  in  or  above 
the  alto-stratus  level,  or  about  6400  meters  elevation.  At 
Willemstad  and  Port  of  Spain,  with  mean  latitude  of  12°,  the 
reversal  is  in  the  cirro-cumulus  level,  at  about  8000  meters 
elevation.  This  is  shown  on  the  northern  winter  branch  of 
fig.  62,  "  Mean  altitudes  at  which  the  westward  drift  reverses 
to  the  eastward  drift  in  the  Tropics. " 


FIG.  62. — Mean  altitudes  at  which  the  westward  drift  reverses  to  the 
eastward  drift  in  the  Tropics. 

An  examination  of  the  vectors  for  the  summer  group  of 
months  indicates  that  generally  there  is  a  tendency  to  rever- 
sal in  the  cirrus  and  cirro-stratus  levels,  at  about  10,000  meters 
elevation.  This,  however,  is  not  definitive,  and  I  have  indi- 
cated the  probable  top  of  the  arch  in  a  broken  line  rather  than 
to  positively  assign  the  limit.  The  summer  westward  circula- 
tion is  very  feeble  throughout  the  column  from  the  sea  level  at 
least  to  the  10,000-meter  level,  and  it  may  be  that  it  extends 
even  to  a  higher  level  over  the  effective  thermal  equator,  which 
lags  about  forty-five  days  behind  the  position  of  the  sun  in 
latitude.  In  the  very  complex  circulation  actually  existing  in 
the  Tropics  it  is  not  possible  to  make  very  exact  statements 
regarding  such  a  loosely  defined  boundary  as  that  which 
really  separates  the  eastward  and  westward  currents  of  the 
atmosphere  underneath  the  sun.  The  calms  of  the  thermal 
equator  move  northward  and  southward  with  the  sun,  and  ap- 
parently the  westward  drift  extends  upward  unbroken  to  about 
six  miles,  though  at  that  level  there  are  evidences  that  the 
eastward  drift  is  making  itself  felt.  The  east  and  west  cur- 
rents play  against  each  other  at  these  high  levels  in  a  some- 
what irregular  manner. 

THE     LEVELS    OF    MAXIMUM    HORIZONTAL    VELOCITY. 

An  examination  of  Charts  XIII  A,  XIII  B,  XIII  C,  figs.  33  to 
43,  brings  out  clearly  the  levels  of  the  maximum  horizontal  cur- 
rents. The  circulation  generally  increases  in  westward  veloc- 
ity from  the  surface  to  the  strato-cumulus  level,  then  falls  off 
to  a  minimum  in  the  alto-stratus  level,  where  the  direction  is 
irregular,  and  then  increases  to  a  maximum  eastward  velocity 
in  the  cirrus  level.  The  stations  of  Cienfuegos  and  Santiago, 
Cuba,  together  with  Kingston  and  Santo  Domingo,  give  rela- 
tively small  resultant  velocities  in  the  lower  levels,  from 
wind  to  cumulus,  as  compared  with  Havana,  San  Juan,  and  the 
southeastern  group,  Basseterre,  Roseau,  Bridgetown,  Port  of 
Spain,  and  Willemstad.  The  former  group  of  stations  develop 
greater  irregularity  in  their  azimuth  directions  than  do  the 
latter  group,  and  consequently  their  resultants  are  much 
diminished  in  magnitude.  This  probably  indicates  some  ac- 
tion of  the  continental  mass  of  North  America  in  disturbing 
the  westward  drift,  which  prevails  steadily  in  the  Windward 
Islands,  and  in  changing  its  general  direction  from  the  south- 
east, which  is  the  natural  flow  from  the  trades,  to  the  northeast 
in  that  region.  The  strato-cumulus  level  in  the  more  eastern 
stations  has  a  powerful  westward  current,  which  falls  off  de- 
cidedly in  the  vicinity  of  Cuba.  On  the  other  hand  the  north- 


eastward  or  eastward  velocity  in  the  three  upper  levels— cirro- 
cumulus,  cirro-stratus,  and  cirrus — is  at  a  maximum  over  the 
Cuban  stations,  and  tends  to  diminish  toward  the  southeast; 
that  is,  from  the  Antilles  to  Port  of  Spain.  The  trade  from  the 
southeast  holds  quite  uniformly  in  the  lower  levels  of  the  east- 
ern group  of  stations,  and  the  northeastward  upper  trade  pre- 
vails in  the  upper  levels  of  the  western  group.  Between  the 
lower  and  the  upper  levels  there  is  a  region  of  transition  whose 
nature  is  quite  clearly  indicated.  At  Port  of  Spain  the  south- 
east trade  prevails  throughout  the  year  with  maximum  in  the 
cuinulo-stratus  level,  diminishing  and  partially  reversing  in 
the  cirro-stratus  and  cirrus  levels.  At  Willemstad,  Bridge- 
town, and  Roseau  there  is  an  exclusively  northern  component 
in  the  alto-cumulus  and  alto-stratus  levels.  At  Basseterre  and 
San  Juan  this  component  becomes  northwestward  or  shows 
signs  of  reversing.  At  Kingston  and  Santiago  the  azimuths 
are  irregular  and  the  velocities  small,  and  at  Cienfugos  and 
Havana  the  eastward  drift  practically  dominates.  Beyond 
these  statements  it  is  not  very  safe  to  go  at  present.  The  cir- 
culation is  complex  and  depends  largely  upon  the  relation  of 
the  Atlantic  high  area,  belonging  to  the  general  high  pres- 
sure belt  of  the  Northern  Hemisphere,  to  the  adjacent  conti- 
nents. The  normal  system  seems  to  be  like  that  of  Willemstad, 
Bridgetown  as  corrected,  and  Roseau,  where  the  movements 
from  the  southeast  in  the  lower  levels  change  to  movements 
from  the  south  in  the  middle  levels  and  from  the  southwest  in 
the  higher  levels.  The  southwest  antitrades  are  conspicuous 
over  Cuba,  but  they  become  west  and  even  northwest  anti- 
trades over  San  Juan  and  the  Windward  Islands.  One  is  sur- 
prised to  find  that  the  southeast  trades  prevail  so  steadily  in  the 
northern  zone,  winter  and  summer,  even  up  to  latitude  +  17°, 
including  Port  of  Spain,  Willemstad,  Bridgetown,  Roseau,  Bas- 
seterre, and  San  Juan.  It  is  evidently  of  primary  importance 
that  meteorologists  should  extend  this  nephoscope  survey  to 
the  Azores,  Ascension  Island,  St.  Helena,  the  South  American 
Continent,  Central  America,  and  Mexico.  The  entire  circula- 
tion of  the  atmosphere  can  thus  be  carefully  determined  by 
means  of  the  method  here  illustrated. 

THE    WINTER    AND    THE    SUMMER    CIRCULATIONS. 

At  a  glance  the  great  contrast  between  the  motions  of  the 
air  in  winter  and  summer  is  apparent.  Over  Havana  the 
northeastward  velocities  are  above  30  meters  per  second  in 
winter,  and  in  the  summer  they  become  about  five  meters  per 
second  and  are  directed  westward.  The  summer  vectors  on 
Chart  XIII  A,  XIII  B,  and  XIII  C  form  an  irregular  broken 
line  which  in  some  cases  become  a  very  good  loop.  This  loop- 
ing or  tangle  in  the  line  is  quite  characteristic  of  the  summer 
vectors  in  the  middle  levels  at  Havana,  Cienfuegos,  Santiago, 
Kingston,  San  Juan,  Basseterre,  and  of  the  vectors  in  the 
high  levels  at  Roseau,  Bridgetown,  Port  of  Spain,  and  Willem- 
stad. These  loops  and  tangles  sometimes  make  it  difficult  to 
determine  from  the  original  observations  what  is  the  true 
mean  curve  to  be  drawn,  because  the  ordinates  are  quite  scat- 
tering and  irregular  in  the  middle  cloud  levels.  In  the  lower 
and  higher  levels  there  was  little  difficulty  experienced  from 
this  cause  in  drawing  the  mean  lines.  As  a  general  principle 
none  of  the  broad  statements  which  meteorologists  have  been 
accustomed  to  make  regarding  the  trade-wind  system  seems 
to  hold  over  a  very  large  region.  The  changes  from  one  lo- 
cality to  another  are  numerous  and  important,  showing  that 
the  circulation  of  the  Tropics  is  really  very  much  localized. 
There  exists  no  system  of  cyclones  and  anticyclones  to  dis- 
turb the  general  circulation,  but  this  circulation  is  itself  much 
more  complicated  than  it  is  in  the  temperate  zone.  The 
dynamics  of  the  two  systems  are  very  different,  and  depend 
upon  a  complex  distribution  of  temperatures  and  pressures. 
Every  effort  should  be  made  to  determine  what  these  are  be- 
fore resorting  to  analytic  discussions,  which  will  be  of  little 
permanent  value  until  all  the  principal  facts  are  known. 


THE    CAUSE    OF    THE    WEST    INDIAN    HURRICAKES. 

The  hurricanes  which  devastate  the  southeastern  districts  of 
the  United  States  in  the  months  from  July  to  October  originate 
in  the  West  Indian  region,  and,  as  much  conjectural  writing 
has  been  published  in  order  to  account  for  them,  it  is  import- 
ant to  throw  what  light  is  possible  upon  the  subject.  In  the 
complex  circulation  shown  to  exist  over  the  Carribean  Sea,  it 
is  easy  to  suppose  that  gyratory  local  circulations  can  be  set 
up  which  will  develop  into  cyclonic  action.  The  summer  cir- 
culation is  irregular,  as  befits  a  belt  of  calms  such  as  prevail 
in  the  doldrums,  or  it  has  a  feeble  westward  direction.  In 
the  winter  this  motion  has  become  powerfully  eastward  in  the 
upper  levels,  in  consequence  of  the  overspreading  of  the  cold 
sheet  of  air  from  the  temperate  zone,  which  is  controlled  by 
the  eastward  drift  of  higher  latitudes.  In  the  autumn,  espe- 
cially in  September,  a  marked  change  takes  place,  by  which 
the  stagnant  or  westward  moving  air  is  sharply  propelled  east- 
ward. This  is  seen  by  examining  the  months  of  August,  Sep- 
tember, and  October,  in  the  alto-stratus  and  the  higher  levels 
on  Charts  XIII  A,  XIII  B,  XIII  C,  figs.  33,  34,  35,  38,  39,  40, 
and  41,  for  Havana,  Cienfuegos,  Santiago,  San  Juan,  Basseterre, 
Roseau,  and  Bridgetown.  This  indicates  the  locality  where 
hurricanes  are  especially  generated,  and  agrees  with  otherwise 
well  known  facts.  They  seldom  occur  as  far  south  as  Port  of 
Spain  and  Willemstad,  but  at  these  stations  there  is  no  indi- 
cation of  a  sharp  reversal  in  the  cloud  region.  The  level?:  from 
alto-stratus  to  cirrus,  from  four  to  six  miles  high,  are  those  chiefly 
concerned  in  causing  the  hurricane  formation.  The  lower  levels 
do  not  have  the  same  reversal  currents,  but  their  vectors  are 
very  steadily  directed  from  the  southeast  to  the  northwest 
throughout  this  season  of  the  year.  A  hurricane  is  built  up 
on  exactly  the  same  mechanical  principle  as  a  tornado,  namely, 
by  the  conflict  of  two  currents  flowing  together  from  differ- 
ent directions  and  having  different  temperatures,  only  the 
hurricane  is  much  deeper  than  the  tornado,  the  hurricane 
forming  a  tube  from  four  to  six  miles  long,  while  the  tornado 
tube  seldom  exceeds  one  mile  in  length.  In  the  tornadoes  of 
the  United  States  the  cool  wind  from  the  northwest  flows 
against  and  over  the  warm  current  from  the  south  or  south- 
east as  they  meet  in  the  central  valleys.  Between  them,  at  the 
height  of  about  one  mile,  a  vortex  tube  is  formed,  which,  by 
its  gyratory  action,  extends  downward  through  the  lower 
strata,  which  latter  must  be  in  a  more  or  less  quiescent  state 
or  else  drifting  slowly  forward  from  top  to  bottom.  In  the 
case  of  the  hurricane  in  the  high  levels  we  have  the  cool  east- 
ward drift  of  autumn  strengthening  and  spreading  into  the 
tropic  zone,  with  a  northeastward  or  eastward  current,  as  shown 
at  Havana,  Cienfuegos,  Santiago,  San  Juan,  Basseterre,  Roseau, 
and  Bridgetown,  Charts  XIII  A,  XIII  B,  and  XIII  C.  This 
meets  the  southeast  trade  with  currents  moving  northwest- 
ward, as  shown  at  Willemstad  and  Port  of  Spain,  Charts  XIII  C, 
figs.  42  and  43,  and  between  them  a  gyration  is  set  up  which 
penetrates  downward  four  to  six  miles,  and  so  produces  a  vor- 
tex tube  of  large  dimensions  and  great  power  at  the  surface, 
such  as  hurricanes  exhibit.  This  conclusion  is  an  exact  agree- 
ment with  the  results  obtained  in  the  Report  of  the  Chief  of 
the  Weather  Bureau,  1898-99,  vol.  2,  as  given  on  chart  35  for 
the  tropical  hurricane  and  described  on  page  457.  It  was 
there  shown  that  the  vectors  of  motion  in  the  cirrus  level  re- 
quire the  existence  of  a  vortex  tube  at  least  five  miles  long. 
The  usual  drift  of  hurricanes  from  the  place  of  generation  is 
at  first  westward  or  northwestward,  and  this  is  because  they 
are  carried  along  with  the  prevailing  currents  in  the  lower  and 
middle  levels.  It  seems  then  that  hurricanes  build  up  in  the 
higher  levels  by  the  counterflow  of  currents  there  prevailing, 
that  they  penetrate  through  four  to  six  miles  of  lower  strata 
to  the  surface,  and  are  borne  along  westward  by  entanglement 
in  the  lower  currents  through  which  they  penetrate.  When 
these  change  their  direction  to  the  northward  and  northeast- 


34 


ward  the  hurricane  track  recurves  with  them.  On  the  other 
hand  the  hurricane  itself  disappears  in  higher  latitudes  and 
is  transformed  into  a  shallow  cyclone,  because  there  the  coun- 
tercurrent  flow  in  the  higher  levels  ceases.  These  conclusions 
can  be  further  illustrated  by  reference  to  Charts  XIV  A,  XIV  B, 
and  XIV  C,  mentioned  above. 

APPROXIMATE    NORMAL   CIRCULATION    IN    THE   WEST   INDIES   DURING  THE 
WINTER    AND    SUMMER,    RESPECTIVELY. 

On  Charts  XIV  A,  XIV  B,  XIV  C,  figs.  44  to  61,  which  show 
the  average  normal  circulation  in  the  West  Indian  district  of 
the  Tropics,  special  attention  is  directed  to  the  vectors  in  the 
four  upper  levels — alto-stratus,  cirro-cumulus,  cirro-stratus, 
and  cirrus — for  the  summer  months,  figs.  44  to  52.  These  charts 
were  drawn  by  inspecting  all  the  available  data  from  the  eleven 
stations  and  carefully  determining  the  most  probable  mean  vec- 
tors that  would  make  a  natural,  well-balanced  system,  wherein 
irregularities  due  to  imperfect  observations  would  be  rectified. 
A  comparison  with  the  vectors  of  Charts  XII  A,  XII  B,  and 
XII C  shows  that  the  changes  which  have  been  introduced  are 
all  of  a  minor  nature,  and  it  is  supposed  that  a  larger  number 
of  observations  with  the  nephoscopes  would  produce  a  system 
of  vectors  very  closely  approximating  those  here  adopted.  In 
the  lower  levels,  from  the  surface  wind  up  to  and  including 
the  alto-cumulus  level,  the  currents  are  similar,  except  that  in 
the  strato-cumulus  level  the  velocity  is  at  a  maximum.  From 
this  level  it  diminishes  both  upward  and  downward. 

It  should  be  remembered  that  in  discussing  the  nephoscope 
observations  of  1896-97  for  the  strictly  cyclonic  and  anti- 
cyclonic  components  in  the  circulation  of  the  middle  latitudes, 
we  reached  the  same  result  regarding  the  prevailing  level  of 
maximum  velocity,  namely,  that  the  maximum  velocity  is  in  the 
strato-cumulus  level.  Compare  chart  68,  page  625,  Report  of 
the  Chief  of  the  Weather  Bureau,  1898-99,  Vol.  II. 

In  the  upper  levels  of  the  Tropics,  on  the  other  hand,  a 
new  circulation  is  prevailing,  which  is  peculiarly  interesting 
in  connection  with  the  causes  that  generate  hurricanes.  In- 
stead of  one  single  westward  drift,  as  in  the  five  lower  levels, 
there  exist  two  countercurrents  in  the  four  upper  levels.  The 
western  group  of  stations — Havana,  Cienfuegos,  Santiago,  and 
Kingston — have  their  vectors  pointing  southward;  the  eastern 
group  of  stations — that  is,  Santo  Domingo,  San  Juan,  Basse- 
terre, Roseau,  Bridgetown,  Port  of  Spain,  and  Willernstad — 
have  vectors  pointing  generally  northward.  Between  them 
there  is  a  distinct  region  of  counterflow,  and,  consequently,  an 
area  of  low  pressure.  If  we  assume  that  in  the  upper  strata, 
where  the  mechanical  friction  is  a  very  small  quantity,  and 
where  the  internal  mixing  from  local  minor  cyclones  is  negli- 
gible, the  vectors  are  directed  nearly  parallel  to  the  isobars, 
then  we  can  easily  construct  their  configuration,  though  we 
can  not  assign  numerical  values  to  them  without  further  in- 


vestigations. On  the  eastern  side  there  is  a  high  area,  which 
is  a  portion  of  the  western  end  of  the  prevailing  Atlantic  high 
pressure.  On  the  western  side  there  is  another  high  pressure 
area,  whose  origin  is  not  so  easy  to  understand.  Over  the 
North  American  Continent  in  summer  the  heated  surface  con- 
ditions produce  a  general  low  pressure  area  in  the  lower 
strata,  and  simultaneously  a  high  pressure  area  in  the  upper 
strata.  It  is  very  likely  that  the  western  high  pressure  in  the 
upper  strata  over  the  West  Indies  is  really  the  southern  ex- 
tension of  the  continental  high  pressure  area  prevailing  in 
summer  over  the  United  States.  Some  further  computations 
on  our  nephoscope  observations  in  the  United  States  will  be 
required  to  determine  the  exact  facts. 

Between  these  two  high  pressure  areas  in  the  West  Indies 
there  exists  a  low  pressure  area,  with  countercurrents  on 
either  side,  so  that  all  the  conditions  are  present  that  are 
needed  to  produce  a  cyclone  in  the  upper  strata.  If  the  prevail- 
ing pressures  and  currents  become  intensified  at  any  time,  the 
high-level  cyclone  is  strengthened,  and  it  then  penetrates  with 
its  large  vortex  tube  to  the  surface  as  a  regular  hurricane. 
The  entire  circulating  structure  is  borne  along  northwestward 
in  the  prevailing  drift  of  the  lower  levels  till  it  recurves  in  the 
southeastern  part  of  the  United  States.  It  is  evident  that  the 
locality  of  the  formation  of  the  center  of  cyclonic  motion  may 
shift  eastward  and  westward  over  the  West  Indian  region,  de- 
pending upon  the  state  of  the  atmosphere  at  the  time,  the  posi- 
tion of  the  two  great  high  pressure  areas,  and  the  conflicting 
currents  in  action.  The  normal  type  here  produced  is  in 
reality  made  up  of  numerous  fluctuations  on  either  side  of  the 
mean.  In  forecasting  for  hurricane  conditions  it  becomes 
necessary  to  watch  carefully  the  motions  of  the  four  upper 
cloud  levels,  in  order  to  learn  the  practical  signs  foreshadow- 
ing such  a  hurricane  condition. 

On  Charts  XIV  B,  XIV  C,  figs.  53  to  61,  "  Normal  vectors 
for  winter,"  the  interest  is  of  a  different  character  from 
that  explained  in  connection  with  the  summer  type.  Here  it 
is  the  reversal  from  the  westward  drift  of  the  lower  strata  to 
the  eastward  drift  of  the  upper  strata.  From  the  surface  up 
to  and  including  the  strato-cumulus  level  the  configuration  is 
generally  the  same  throughout  the  West  Indian  region,  Then 
the  reversal  vectors  first  set  in  at  the  western  stations,  Havana, 
Cienfuegos,  Santiago,  in  the  alto-cumulus  and  alto-stratus 
levels;  the  other  stations  become  involved  later  in  the  higher 
cirro-cumulus,  cirro-stratus,  and  cirrus  levels,  where  the  regular 
antitrades  prevail.  The  azimuths  of  the  higher  vectors  show 
that  the  northward  component  nearly  vanishes  in  the  cirrus 
level  over  the  eastern  stations.  It  will  be  necessary  for  mete- 
orologists to  outline  the  eastern  portions  of  the  Atlantic  high 
area  in  the  levels  up  to  six  miles  before  executing  conclusive 
discussions  of  the  important  dynamic  problems  suggested  by 
these  vectors. 


VI.— THE  CIRCULATION  IN  CYCLONES  AND  ANTICYCLONES,  WITH  PRECEPTS  FOR  FORECASTING  BY  AUXILIARY  CHARTS  ON  THE 

3500-FOOT  AND  THE  10,000-FOOT  PLANES. 


In  my  paper  on  "The  mechanism  of  countercurrents  of  dif- 
ferent temperatures  in  cyclones  and  anticyclones,"  MONTHLY 
WEATHER  REVIEW,  February,  1903,  some  account  was  given  of 
the  construction  of  the  auxiliary  charts  of  barometric  pres- 
sures for  the  United  States  on  the  3500-foot  and  the  10,000- 
foot  planes,  to  correspond  with  the  daily  weather  map  on  the 
sea-level  plane.  These  new  charts  have  been  prepared  daily 
since  December  1,  1902,  and  they  have  been  carefully  studied 
from  that  time  with  two  purposes  in  view,  the  results  of  the 
examination  being  briefly  stated  in  this  paper,  while  the  more 
detailed  explanation  will  appear  in  Volume  II  of  the  Annual 
Report  of  the  Chief  of  the  Weather  Bureau  for  1903^4.  The 
first  purpose  concerns  the  information  they  have  given  as  to 
the  actual  circulation  in  the  strata  above  the  surface,  and  its 
relation  to  several  theories  which  have  been  advanced  to  ac- 
count for  these  local  circulations,  and  the  second  has  regard 
to  the  derivation  of  precepts  useful  in  forecasting  the  weather. 
It  is  quite  impossible,  I  presume,  to  convey  to  one  who  has 
not  had  an  opportunity  to  see  these  upper-level  charts  any 
adequate  impression  of  their  significance  to  modern  meteorol- 
ogy, or  of  the  transformations  which  take  place  in  the  structure 
of  the  three  systems  of  isobars,  as  a  cyclone  passes  over  the 
United  States.  They  must  be  taken  together  for  the  best  re- 
sults, and  the  study  of  their  mutual  configurations  and  varia- 
tions affords  us  an  insight  into  the  true  cause  of  storm  forma- 
tion, which  is  decisive  as  to  their  nature,  and  is  of  especial  in- 
terest to  the  intelligent  forecaster. 

THE    STRUCTURE    OF    THE    ISOBARS    AT    DIFFERENT    LEVELS. 

In  the  MONTHLY  WEATHER  REVIEW  for  January  and  February, 
1903,  several  examples  were  given  of  the  configuration  of  the 
isobars  in  cyclones  on  the  three  reference  planes,  and  also  of 
their  resolution  into  two  components,  namely,  the  normal  iso- 
bars of  the  month  and  the  abnormal  or  disturbance  isobars, 
which,  when  added  to  the  normal  isobars,  produce  the  observed 
isobars  of  the  date.  The  normal  monthly  isobars  were  taken 
from  the  Barometry  Report,  1900-1901,  and  the  separation  of 
the  two  systems  was  made  by  means  of  a  graphical  construc- 
tion. Our  purpose  was  to  separate  the  strictly  local  disturb- 
ance circulation  from  the  general  circulation,  so  far  as  the 
isobars  are  concerned,  and  to  compare  this  component  of  the 
pressure  with  the  wind  vectors  which  had  been  derived  from 
the  cloud  observations  of  1896-97,  a  summary  of  which  was 
given  in  the  MONTHLY  WEATHER  REVIEW  for  March,  1902.  To 
illustrate  this  process,  Charts  XII  and  XIII  for  February  3, 1903, 
are  introduced. 

Chart  XII,  fig.  63,  gives  the  sea-level  isobars  as  on  the 
weather  map  for  February  3,  1903 ;  fig.  64  gives  in  black  the 
isobars  of  the  same  date  on  the  3500-foot  plane,  and  in  red 
those  on  the  10,000-foot  plane.  The  components  are  given 
on  Chart  XIII,  where  the  black  lines  on  fig.  65  give  the  normal 
system  for  February  on  the  3500-foot  plane  undisturbed  by 
cyclonic  action,  and  the  red  lines  the  abnormal  system,  which, 


when  added  to  the  normal,  produces  the  black  lines  of  fig.  64 
The  black  lines  in  fig.  66  give  the  normal  and  the  red  lines 
the  abnormal  system  on  the  10,000-foot  plane.  Since  the  dis- 
turbance on  the  sea-level  plane  is  not  much  affected  by  the 
normal  system,  the  resolution  into  components  is  omitted.  It 
follows  that  we  shall  properly  compare  together  fig.  63  and 
the  abnormal  systems,  or  red  lines,  on  figs.  65  and  66  when 
discussing  the  theory  of  cyclonic  gyrations.  In  the  course  of 
the  year  numerous  modifications  of  the  fundamental  type 
occur,  but  in  all  cases  it  is  not  difficult  to  detect  what  this 
modification  is  and  to  be  certain  that  we  are  dealing  with  one 
simple,  natural  structure  to  which  every  theory  must  conform 
to  become  acceptable. 

In  order  that  we  may  concentrate  attention  more  closely 
upon  the  primary  structure,  which  suffers  numerous  modifica- 
tions in  the  local  circulation,  an  example  is  given  on  Chart  XIV 
of  a  typical  system  of  the  normal  and  of  the  abnormal  iso- 
bars, such  as  occur  in  a  well  developed  cyclone  for  the  month 
of  February,  upon  which  to  base  certain  conclusions  that 
are  in  fact  sustained  by  the  entire  series,  without  any  sort  of 
contradictory  or  conflicting  evidence.  Chart  XIV,  figs.  67,  68, 
and  69  give  the  normal,  and  figs.  70,  71,  and  72  the  abnormal 
isobars  on  these  planes. 

The  discussion  can  not  be  considered  complete  without  join- 
ing with  the  isobars  the  corresponding  systems  of  isotherms 
at  all  three  levels,  but  in  the  present  stage  of  our  study  it  is 
not  possible  to  do  this  with  accuracy  in  the  higher  levels. 
The  temperature  conditions  in  the  upper  strata  can  not  be 
reached  by  direct  computation,  as  has  been  done  with  the  iso- 
bars, until  a  very  much  more  extended  series  of  actual  meas- 
urements than  we  now  possess  has  been  made  by  means  of 
balloon  and  kite  ascensions,  such  as  are  proposed  at  the  Mount 
Weather  Observatory.  On  this  account  the  resolution  of  the 
isotherms  into  their  normal  and  abnormal  exponents  is  now 
limited  to  the  sea-level  plane,  or  rather,  to  the  surface  of  the 
United  States.  An  example  is  taken  from  the  map  of  Febru- 
ary 27,  1903,  which  is  reproduced  on  Chart  XV,  figs.  73  and 
74,  where  the  isotherms  are  printed  in  red.  The  temperature 
components  are  formed  by  exactly  the  same  method  as  was 
employed  in  resolving  the  isobars,  the  normal  temperature  sys- 
tem being  taken  from  the  Barometry  Report.  Fig.  73  gives  the 
weather  map,  and  fig.  74  the  normal  and  abnormal  isotherms. 

THE    GEOMETRICAL    CONSTRUCTION    OF   HIGH   AND    LOW  PRESSURE    AREAS, 

From  the  study  of  the  isobars  on  the  three  planes,  it  is  possible 
to  draw  several  important  conclusions  which  have  the  value 
of  general  principles.  It  was  shown  in  the  MONTHLY  WEATHER 
REVIEW  for  February,  1903,  fig.  25,  "The  formation  of  local 
anticyclones  and  cyclones  in  the  general  circulation  about 
the  poles,"  that  the  distribution  of  pressure  commonly  ob- 
served can  be  approximately  reproduced  by  the  superposition 
of  systems  of  concentric  circles,  representing  positive  and 
negative  local  additions  to  the  general  circles  of  the  hemis- 

35 


36 


phere  concentric  about  the  pole.  The  charts  of  the  year  1903 
give  the  actual  shape  of  the  lines  as  they  occur  in  nature, 
which  are  seldom  concentric  circles  in  their  form.  In  the 
cyclone  they  more  nearly  resemble  ellipses,  which  as  a  family 
have  one  focus  in  common,  the  other  retreating  as  the  area  of 
the  ellipse  enlarges.  In  other  words  the  isobars  are  crowded 
together  on  one  side  of  the  cyclone,  as  the  northeastern,  and 
opened  on  the  opposite  side.  I  explain  this  fact  from  the  cir- 
cumstance that  the  warm  area  and  greater  bouyancy  of  the 
air  is  on  the  crowded  quadrant,  so  that  a  stronger  tendency 
to  true  vortex  action  exists  there  than  011  the  cold  side,  where 
the  downward  flow  of  the  air  tends  to  diminish  vortex  motion, 
that  is  to  decrease  the  abnormal  pressure  gradients.  This  can 
be  verified  by  examining  the  abnormal  isotherms  of  Chart  XV, 
for  February  27, 1903.  The  major  axis  of  the  system  of  ellipses 
is  pointed  forward  of  the  axis  of  symmetry  of  the  entire  cir- 
culation, generally  the  meridian,  and  makes  an  angle  a.  with 
it.  All  possible  relations  of  the  ellipses  to  the  axes  chosen,  as 
x  =  the  meridian,  positive  southward,  y  =  the  parallel,  positive 
eastward  are  contained  in  the  equation, 

(1  —  e2  sin8  «)  y2  —  2  e2  sin  a  cos  a  xy  +  (1  —  e2  cos2  a)  #2 
+  (2  e2  d  sin  a  —  2  b)  y  +  (2  e2  d  cos  a  —  2  a)  x 
&J  _  e2  d2)  =  0. 


FIG.  75.— The  general  ellipse. 
Let  (o  6)  —  the  coordinates  of  the  focus  F. 

(x  y)  =  the  coordinates  of  any  point  on  the  curve. 
d  —  distance  of  the  directrix. 

a  —  the  angle  that  transverse  axis  (PP=  A)  makes  with  x. 
A  —  the  length  of  the  transverse  axis. 
B  =  the  length  of  the  conjugate  axis. 

(^3 Jfl\    1 
A'      I 
FC  —  A  e  =  distance  focus  to  center. 

FP  =  A  (1  =f  e)  =  distance  focus  to  vertex. 

A 
PD  —  —  (1  =F  e) =  distance  vertex  to  directrix. 

6 
A 

CD  —     =  distance  center  to  directrix. 

C 

A  much  simplified  case  occurs  where  d  =  0,  «  =  0,  where 
the  directrix  is  the  axis  y,  and  the  transverse  axis  coincides 
with  the  axis  x.  For  example,  if  e  =  0.57,  d  =  0,  a  =  10,  b  =  0, 
sin  a  =  0,  cos  a  =  1,  the  equation  becomes, 


?/2  +0.67^  — 

The  solution  gives  such  point  pairs  as  (6.4,  0),  (8,  4.14), 
(10,  5.75),  (12,  6.60),  (15,  7.01),  etc.,  from  which  the  ellipse  is 
to  be  plotted. 

To  illustrate  the  composition  of  two  systems  of  isobars  we 
take  that  of  right  lines  and  circles.  ' 

Let  R  =  the  radius  of  the  circle, 
(a,  1)  =  the  coordinates  of  the  center, 
(x,  y)  =  the  coordinates  of  any  point  on  the  circle. 

The  general  equation  of  the  circle  is, 

(x-ay+(y-bY  =  IP. 

If  we  take  b  =  0  and  transpose  the  terms, 
7/z=  —  x*  +  2ax  +  E2  —  a2. 

The  equation  of  the  condition  of  the  isobar  which  is  the  re- 
sultant of  successive  circular  abnormal  isobars  added  to  suc- 
cessive right  line  normal  isobars,  is  that  the  sum  of  certain 
pair  numbers  shall  be  constant  on  the  same  line.  Thus, 
A  +  ft  =  constant,  where  A  =  n  x  =  some  multiple,  n,  of  the  co- 
ordinate x,  and  B  =-the  gradient  number  on  the  circles.  For 
example,  take  the  gradient  on  the  normal  right  lines  one-half 
that  on  the  normal  circles,  so  that  n  =  \,  which  is  about  the 
average  in  highly  developed  storms.  Take  successive  circles, 
E  =  6,  5,  4,  3,  2,  whose  gradient  numbers  are  respectively 
B  =  0,  —  l,  —  2,  —  3,  —  4.  Take  a  =  6,  A  =  1  x,  A  +  B  =  0  for 
the  0-line  and  n  =  \. 

TABLE  15. — Form  for  computing  the  coordinates  of  the  resultant  curve. 


R. 

B. 

^=i, 

*=-^"+»-*. 

2/  coordinate. 

8 

zz6 

B 

—    o 

x  =  0 

tf  =         0+   0  +  36  —  36=  0 

y—     o 

R 

=  5 

Ji 

=  —  1 

v.  —  2 

tf  —  —    4  +  24+25—36=   9 

i/  =±3.00 

B 

=  4 

B 

=  —  2 

a;  zz4 

?/'  =  —  16  +  48  +  16  —  36  zz  12 

2/  =  ±  3.47 

R 

zz  3 

Jl 

=  —  3 

g  —  (i 

3^=  —  36+72+   9  —  36=   9 

2/zz  ±3.00 

R 

zz2 

B 

=  —  4 

*  =  8 

3/2  =  —  64+96+   4  —  36=   0 

y  —        0 

Similarly,  by  taking  the  proper  groups  of  11,  B,  x,  for  the 
—  1,  +1,  —  2,  +2, lines  in  low  and  high  areas,  we  ob- 
tain the  coordinates  of  the  resultants.  The  completed  compu- 
tation is  shown  on  fig.  76.  "  Right  lines  and  circles,  where  the 
gradients  are  twice  as  great  on  the  circles  as  on  the  right 
lines."  The  preceding  example  plots  the  0-line  of  the  low 
area  as  will  be  seen  by  the  pair  points  (0,  0),  (2,  ±3.00), 
(4,  ±3.47),  (6,  ±3.00),  (8,  0). 


FIG.  76. — Bight  lines  and  circles  where  the    gradients  are    twice   as 
great  on  the  right  lines. 

In  this  manner  the  simple  cases  can  be  readily  handled  ana- 
lytically, and  the  principal  is  theoretically  to  be  extended  to 
all  such  groupes  of  curves  as  can  be  reduced  to  a  mathemati- 
cal expression.  It  is,  however,  evident  that  we  can  not  obtain 
the  equations  for  the  observed  isobars  except  in  simplified 
cases,  and  that  generally  a  graphical  solution  is  all  that  can 


37 


be  employed.  Practically,  one  takes  a  sheet  of  normal  isobars 
and  places  over  it  a  sheet  of  observed  isobars.  Then,  the  dif- 
ferences at  the  points  of  intersection  are  marked  in  the  sense 
that  so  many  tenths  of  an  inch  must  be  added  to  or  sub- 
tracted from  the  normal  isobar  to  produce  the  observed  isobar 
at  that  point.  By  joining  up  the  points  of  equal  difference 
numbers  the  system  of  the  abnormal  isobars  for  the  day  is  ob- 
tained. The  axes  of  the  negative  areas,  L,  have  one  nearly 
equal  angle,  «,  with  the  meridian,  but  the  axes  of  the  positive 
areas,  H,  H,  become  convergent  upon  two  cusps,  0,  G,  fig.  70, 
Chart  XIV,  which  tend  to  unite  over  a  saddle,  S,  of  rela- 
tively high  pressure,  separating  the  cyclone  proper  L  from 
the  wide  spread  region  of  low  pressure  lying  beyond  the 


axis. 


THE    CUSP    FORMATION  AND    ITS    CHANGES. 


Between  the  isobars  marked  0  and  — 1,  in  all  levels,  there 
is  a  line  of  pressure  which  is  exactly  the  same  throughout  its 
extent,  as  indicated  by  the  line  of  dots  on  fig.  11,  3500-foot 
level,  MONTHLY  WEATHEK  REVIEW,  January,  1903.  The  rounded 
cusps  of  the  typical  abnormal  isobars  of  Chart  XIV  become 
sharp  cusps  at  that  pressure,  in  contact  at  a  central  point  on 
the  saddle,  and  from  this  line  the  pressure  falls  in  two  direc- 
tions, but  rises  in  two  other  directions  as  shown  on  the  typical 
figures.  It  is  evident  that  by  raising  or  lowering  the  pressure 
of  the  entire  cyclonic  region,  the  number  of  the  closed  curves 
inside  the  cusps  can  be  diminished  or  increased.  For  instance 
in  intensifying  the  cyclone  the  existing  cusps  advance  and  flow 
together,  and  then  separate  into  an  additional  closed  curve 
and  an  additional  line  at  the  top  of  the  figure.  If  the  pres- 
sure is  diminishing,  an  inclosed  curve  advances  to  meet  an 
outside  line,  and  joining  with  it  produces  a  new  cusp,  but  at 
the  sacrifice  of  an  inside  closed  isobar.  Thus,  there  is  contin- 
ued building  or  destroying  of  the  closed  central  isobars  going 
on  in  the  action  of  the  cyclones  and  anticyclones  of  the  atmos- 
phere in  proportion  to  the  energy  of  the  circulation  at  any 
given  level.  Now,  011  passing  from  one  level  to  another  along 
the  same  vertical  we  find  a  similar  increase  and  decrease  of 
the  cusp  action,  showing  that  in  the  same  cyclone  this  differ- 
ence of  strictly  cyclonic  circulation  exists. 

The  general  rule  is  that  the  number  of  closed  isobars  steadily 
diminish''*  ici/h  the  height,  as  shown  on  Chart  XIV.  Our  maps 
give  this  structure  in  all  stages  of  the  development,  from 
energetic  storms  with  power  to  penetrate  to  considei'able 
heights,  to  shallow  storms  which  have  become  entirely  depleted 
within  two  miles  of  the  ground.  In  the  winter  the  cyclonic 
circulation  is  exclusively  in  the  lower  strata,  and  is  soon  stripped 
away  by  penetrating  the  swiftly  moving  general  circulation  of 
the  eastward  drift.  A  remarkable  fact  has  been  developed, 
namely,  that  as  the  warm  weather  comes  on  and  the  power  of 
the  eastward  general  currents  diminishes,  the  structure  of  the 
cusps  and  closed  isobars  is  maintained  at  very  much  higher 
elevations.  Thus,  in  April  and  May  the  10,000-foot  level  is  as 
much  involved  as  the  3500-foot  level  is  in  January  and  Febru- 
ary. I  explain  this  by  two  facts:  first,  that  the  general  cur- 
rents in  the  lower  levels  of  January  and  February  have  re- 
treated to  higher  elevations  in  April  and  May,  carrying  the 
cyclonic  structure  with  them;  second,  that  in  the  warm 
months  there  is  much  more  surface  heat  to  dispose  of  in 
cyclonic  action  than  in  the  winter,  but  that  it  must  seek  higher 
levels  to  find  the  cold  air  necessary  to  bring  about  the  thermal 
equilibrium. 

In  the  case  of  hurricanes,  as  shown  in  Paper  No.  V  of  this 
series,  the  cyclonic  structure  is  powerful  at  the  height  of  the 
cirrus  levels,  five  to  six  miles  above  the  surface,  and  this  is  in 
confirmation  of  the  results  of  the  Weather  Bureau  cloud  ob- 
servations of  1896-97,  chart  35.  It  was  shown  in  the  same  re- 
port that,  taking  the  entire  year,  the  maximum  cyclonic  circula- 
tion is  in  the  strato-cumulus  level,  two  miles  above  the  surface, 


whereas  in  the  winter  it  is  lower  and  in  the  summer  higher 
than  that  level.  The  cusp  structure  then  diminishes  with  the 
height,  but  there  is  no  instance  in  which  there  is  any  sign  that  the 
closed  isobars  of  low  pressure  reverse  into  closed  isobars  of  high 
pressure  over  the  same  center.  The  closed  isobars  are  of  the 
same  sign  till  they  are  depleted  and  wiped  out  by  penetration 
into  the  eastward  drift.  This  is  a  conclusion  without  contra- 
diction, and  it  is  fundamental  to  cyclonic  theories.  Since  the 
cyclonic  circulation  has  an  inward  component,  as  is  well  known 
to  be  the  fact,  in  the  lower  levels,  it  follows  that  it  must  have 
an  inward  component  in  all  levels  until  it  is  absorbed  in  the 
upper  strata.  There  is  no  reversal  of  the  gradient  system  of 
isobars  in  the  higher  level  as  compared  with  the  lower  level, 
and  there  can  be  no  outflow  in  the  upper  level  of  the  cyclone  proper 
unless  it  can  be  shown  that  there  is  a  reversal  of  the  isobars. 
The  theoretical  discussions  which  assume  a  reversal  of  gra- 
dients in  the  upper  portions  of  the  cyclones  have  no  founda- 
tion in  these  observations,  and  all  such  observations  as  claim 
to  have  found  in  the  cloud  vectors  of  the  upper  levels  a  true 
outflow  (Blue  Hill,  Hildebrandsson  and  others)  have  ap- 
parently not  made  the  separation  between  the  general  and 
the  cyclonic  vectors  with  sufficient  precision  to  escape  this  in- 
correct inference.  It  should  be  remembered  that  the  Weather 
Bureau  has  reached  the  same  result  by  three  independent  lines 
of  research:  (1)  From  the  cloud  observation  at  150  stations  for 
about  twenty-five  years ;  ( 2,)  from  the  theodolite  and  nephoscope 
observations  of  1896-97  as  given  in  the  Cloud  Report;  and 
(3)  from  the  barometric  reductions  now  in  operation  over  the 
United  States  and  Canada.  Furthermore,  the  theoretical  analy- 
sis in  the  Cloud  Report  makes  the  solutions  by  a  reversal  of 
gradients  entirely  improbable,  because  they  depend  upon  the 
existence  of  warm  and  cold  centers,  which  it  is  well  known  do 
not  in  fact  occur.  This  is  easily  seen  by  reference  to  Chart 
XV,  or  to  thousands  of  such  abnormal  charts  in  the  files  of 
the  Weather  Bureau.  I  have  already  explained,  as  in  fig.  28, 
MONTHLY  WEATHEU  REVIEW,  February,  1903,  the  process  by  which 
the  rising  air  in  a  cyclone  is  stripped  off  by  penetrating  the 
eastward  drift,  involving  an  interchange  of  inertia  between  the 
local  and  the  general  circulations.  Also,  some  further  account 
of  the  analytic  conditions  are  contained  in  Paper  No.  Ill  of 
this  series.  It  is  really  very  difficult  to  secure  true  normal 
general  vectors  to  use  in  vector  subtraction  from  the  observed 
vectors  in  all  the  subareas  surrounding  a  low  center,  and  in  all 
the  cloud  strata,  and  it  is  no  wonder  that  the  work  at  a  single 
station  should  be  inadequate  to  such  a  resolution  of  forces. 
Such  work  has  also  been  done  with  the  prepossession  of  the 
old  Ferrel  meteorology  of  cyclones,  which  is  very  incorrect  in 
many  particulars.  An  inspection  of  the  normal  and  abnormal 
isobars  of  Chart  XIV  shows  that  the  normal  isobars  give  in- 
creased gradients  with  the  height,  while  the  abnormal  isobars 
give  diminished  gradients  with  the  height,  and  there  is  no 
reason  why  there  should  be  reversal  in  either  the  cyclone  or 
the  anticyclone,  but  simple  decrease  in  the  abnormal  system 
until  complete  disappearance  occurs  where  the  general  system 
dominates  in  the  high  levels. 

It  should  be  noted  that  while  the  example  of  Chart  XIV 
shows  that  the  saddle  is  directed  northward,  there  are  many 
cases  in  which  the  opening  of  the  cyclone  is  turned  to  the 
other  quadrants.  Thus,  the  saddle  is  found  frequently  in  the 
western  quadrant,  occasionally  in  the  southern  quadrant,  and 
seldom  in  the  eastern  quadrant.  The  opening  may  often 
swing  around  to  the  northeast,  but  it  rarely  points  between 
east  and  southeast.  When  the  saddle  is  to  the  south  in  the 
lower  strata,  it  is  likely  at  the  same  time  to  be  pointing  to  the 
north  in  the  upper  strata,  showing  a  complete  reversal  of  the 
structure  within  the  same  cyclone  as  to  compass  direction, 
but  there  is  never  a  gradient  reversal  from  low  pressure  to 
high  pressure  in  the  cyclone,  or  from  high  pressure  to  low 
pressure  in  the  anticyclone,  so  far  as  known. 


38 


CRITICAL    REMARKS    REGARDING    SEVERAL    THEORIES    OF    CYCLONES    AND 

ANTICYCLONES. 

From  the  data  in  the  possession  of  the  Weather  Bureau  re- 
garding cyclones  and  anticyclones,  it  is  proper  to  lay  down 
the  following  propositions: 

(1).  Currents  of  air  of  different  temperatures  counterflow 
in  the  lower  strata  of  middle  latitudes  to  produce  the  cyclonic 
and  anticyclonic  circulations. 

(2).  The  maximum  and  the  minimum  of  the  abnormal  tem- 
peratures, that  is,  the  warm  and  cold  areas,  are  located  be- 
tween and  not  at  the  centers  of  gyration. 

(3).  The  configuration  of  the  local  isobars,  as  distinguished 
from  the  isobars  that  sustain  the  general  circulation,  is  the 
same  at  all  levels  and  of  the  same  type  as  that  at  the  sea  level. 

(4).  These  closed  isobars  diminish  in  number  with  the  height 
until  they  disappear  in  the  general  circulation  at  moderate 
elevations,  but  they  do  not  reverse  from  low  to  high  pressure 
or  from  high  to  low  pressure  with  the  altitude. 

( 5).  Currents  of  air  stream  continuously  through  the  cyclone 
and  the  anticyclone,  so  that  the  circulation  involves  fresh 
masses  and  not  a  cyclic  return  of  the  same  masses. 

These  principles  seem  to  be  so  thoroughly  established  that 
they  become  criteria  for  the  validity  of  several  proposed  methods 
of  the  analysis  of  cyclones  and  anticyclones,  as  given  in  well- 
known  papers  on  this  subject.  In  case  any  theory  should  con- 
flict with  the  results  of  observations  as  given,  then  the  obser- 
vations must  themselves  be  disproved,  or  else  some  substitute 
found  for  the  theory  in  question.  Several  of  them  were  worked 
out  years  ago,  and  had  not  the  advantage  of  our  modern  ob- 
servations, which  have  materially  modified  the  point  of  view. 

Ferret's  cyclone. — In  this  cyclone  a  bounding  cylinder  is 
drawn  around  the  circulating  mass,  excluding  it  from  contact 
with  fresh  masses  (contra  5);  it  requires  the  maximum  heat 
for  a  warm  center  cyclone,  or  the  minimum  heat  for  a  cold 
center  cyclone  to  be  distributed  symmetrically  about  the  axis 
of  gyration  (contra  2);  the  system  of  isobars  undergoes  re- 
versal along  the  axis,  as  in  the  warm  center  cyclone  from  low 
pressure  at  the  surface  to  high  pressure  above,  with  corre- 
sponding inflow  and  outflow  or  reversal  of  the  radial  compo- 
nents (contra  3  and  4). 

Oberbeck's  cyclone. — This  cyclone  requires  a  symmetrical  dis- 
tribution of  temperature  about  the  center  (contra  2);  an  in- 
crease in  the  vertical  velocity  in  proportion  to  the  height 
above  the  surface  w  =  +  cz,  (contra  4),  whereas  the  diminution 
in  number  of  the  closed  isobars  with  the  height  implies  a  de- 
crease, w  =  —  cz;  a  concentration  of  the  closed  isobars  of  the 
inner  region  near  its  boundary  of  separation  from  the  outer 
region  where  w  =  0,  (contra  3)  since  the  usual  concentration 
in  one  quadrant  and  separation  in  the  opposite  quadrant  is  due 
to  the  location  of  the  warm  and  cold  waves  and  not  to  a 
dynamic  circulation. 

Harm's  cyclone. — The  theory  of  cyclones  as  eddies  in  as  tream 
having  different  velocities  at  the  same  level  requires  greater 
velocity  differences  in  latitude  than  the  general  isobars  which 
sustain  the  eastward  drift  will  admit;  since  the  velocity  differ- 
ences increase  with  the  height,  eddy  cyclones  should  especially 
frequent  the  upper  strata  and  increase  with  the  altitude  (con- 
tra 4),  but  they  disappear  where  they  should  be  strengthen- 
ing; the  temperature  distribution  as  observed  can  not  be  con- 
tinuously maintained  on  purely  hydrodynamic  principles. 

Hildebrandsson's  cyclone. — An  eddy  cyclone  with  inflow  at 
the  bottom  and  outflow  at  the  top  (contra  1,  2,  3,  4)  seems 
inconsistent  with  itself,  if  the  gyratory  velocity  has  opposite 
directions  above  and  below,  as  claimed  to  have  been  indicated 
in  the  diagrams  and  observations  of  the  Blue  Hill  Observatory. 

v.  Bjerknes's  cyclone. — (Compare  Arrhenius's,  Kosmische  Phy- 
sik.)  This  cyclone,deduced  from  the  line  integrations,  requires 
warm  and  cold  centers  superposed  (contra  3),  and  distributed 
symmetrically  about  the  axis  (contra  2);  increase  of  the  closed 


isobars  followed  by  decrease  with  the  height  (contra  4),  and 
varous  internal  circuits  not  found  in  the  Weather  Bureau  ob- 
servations. 

Meinardus  describes  stream  lines  based  upon  the  Oberbeck 
cyclone,  and  the  exposition  has  to  encounter  the  difficulties 
mentioned  above. 

Shaw  describes  a  special  case  motion  quite  in  conformity 
with  the  stream  lines  in  tornadoes,  waterspouts,  and  hurri- 
canes, but  not  in  agreement  with  such  a  complex  circulation  as 
is  found  in  cyclones  of  the  United  States,  and  typified  in 
Chart  XIV. 

If  these  objections  continue  to  be  sustained  by  future  ob- 
servations, it  follows  that  true  analytical  discussion  of  the 
forces  in  cyclones  and  anticyclones  must  avoid  such  mistaken 
assumptions  as  have  been  laid  at  the  basis  of  much  mathemati- 
cal meteorology.  The  actual  circulation  is  really  complex  in 
individual  cases,  and  yet  it  is  not  difficult  to  see  what  in  the 
main  the  leading  principles  must  be.  Further  examination  of 
the  distribution  of  the  temperature  in  the  higher  levels  is  next 
in  the  order  of  the  research. 

THE  CAUSE  OF  THE  COUNTEKCURRENTS  IN  THE  LOWER  STRATA. 

Ferrel's  conception  of  the  general  circulation,  as  derived 
from  a  canal  theory,  where  the  hot  air  of  the  Tropics  rises  and 
flows  toward  the  poles  in  the  higher  levels,  fails  to  give  suf- 
ficient account  of  the  persistent  southerly  winds  in  the  lower 
strata.  Referring  to  Paper  III,  of  this  series,  "  The  problem 
of  the  general  circulation  of  the  atmosphere  of  the  earth," 
MONTHLY  WEATHER  REVIEW,  January,  1904,  the  following  re- 
marks suffice.  If  the  temperature  of  the  Tropics  is  Tt  and  of 
the  temperate  zone  is  T2  in  normal  conditions,  while  the  heat 
energy  of  the  Tropics  is  Qt  we  shall  have  for  the  work, 


in  average  seasonal  relations  on  the  rotating  earth.  Since  the 
solar  insolation  tends  to  raise  T,  to  (T^  +  ^  T^)  in  the  Tropics, 
and  polar  radiation  changes  —  T2  to  —  (  T2  -j-  J  T2),  we  shall 
have  an  increment  of  work, 


W+ 
Where 


by  formula  112,  Cloud  Report.  The  question  depends  upon 
the  expenditure  of  the  work  J  W,  whose  purpose  is  to  restore 
thermal  equilibrium  as  promptly  as  possible. 

The  Weather  Bureau  data  show  that  a  system  of  irregular 
currents  of  warm  air  flow  from  the  Gulf  of  Mexico  upon  the 
United  States  in  the  lower  strata,  and  are  primary  components 
in  the  cyclones,  where  mixing  of  the  currents  of  air  at  differ- 
ent temperatures  is  taking  place.  These  warm  streams  reach 
the  place  of  mixture  by  flowing  a  short  distance  across  the 
general  high  pressure  belt,  where  there  is  no  east  and  west 
velocity  to  complicate  the  action  through  an  interchange  of 
inertia  between  the  normal  masses  and  the  extra  currents.  In 
the  canal  circulation  there  is  on  the  other  hand  great  op- 
portunity for  changes  of  inertia  in  both  senses,  and  this 
the  currents  tend  to  avoid  unless  it  is  forced  upon  them. 
Thus,  the  warm  air  of  the  Tropics  in  rising  first  passes  to 
strata  of  decreasing  velocity;  then,  in  moving  northward,  to 
strata  of  increasing  velocity;  and,  finally,  in  descending  in 
the  temperate  or  polar  zones,  to  strata  of  diminishing  ve- 
locity. It  is  apparent,  therefore,  that  the  over-heated  masses 
in  the  Tropics  seek  the  temperate  zone,  where  they  encounter 
cooler  masses,  by  a  short  and  simple  path  rather  than  by  a 
long  and  very  complex  path.  The  tendency  for  currents  of 
high  temperatures  to  remain  individually  intact  as  long  as  is 
possible  is  an  additional  reason  for  seeking  the  cyclonic  belt 
by  a  direct  path  in  the  lower  and  nearly  quiet  strata. 


39 


Similar  reasoning  applied  to  the  polar  zones  gives  a  suffi- 
cient account  of  the  cold  western  current  that  enters  the 
cyclone.  The  warm  current  on  the  eastern  side  underflows 
the  eastward  drift,  rises  into  it,  and  allows  the  cold  current 
from  the  northwest  to  flow  beneath.  This  starts  a  gyration 
which  is  developed  as  shown  by  the  observations  described, 
and  it  continues  to  act  as  long  as  the  feeding  couutercurrents 
of  different  temperatures  endure.  The  mixture  with  the  east- 
ward drift  propels  the  structure  forward,  and  at  the  same  time 
breaks  up  the  heated  air  coming  from  the  Tropics  into  a  suc- 
cession of  irregular  cyclones  and  anticyclones.  The  mutual 
reactions  between  the  constituent  parts  are  so  numerous  and 
so  subtle  that  it  is  not  easy  to  distinguish  exactly  where  one 
set  of  forces,  as  the  thermodynamic,  ends,  and  another,  as  the 
hydrodynamic,  begins.  This  interplay  is,  no  doubt,  responsible 
for  the  perplexity  that  meteorologists  have  encountered  in 
establishing  the  correct  theory  of  cyclonic  action. 

PRECEPTS    FOB    FORECASTING    WITH    THE    CHARTS    ON    THE    3500-FOOT 
AND    THE    10,000-FOOT    PLANES    AS    AUXILIARIES. 

The  chief  object  in  preparing  auxiliary  pressure  and  tem- 
perature charts  on  two  planes,  3500  feet  and  10,000  feet,  above 
the  sea  level,  was  to  secure  three  sections  through  the  lower 
parts  of  a  storm,  so  that  their  mutual  relations  might  be  studied 
for  the  purpose  of  improving  the  forecasts.  They  have 
proved  to  be  of  interest  not  only  in  theoretrical  meteorology 
but  also  in  forecasting,  as  will  be  more  fully  set  forth  in  the 
full  report.  It  has  been  thought  proper  by  the  Chief  of  the 
Weather  Bureau  to  give  them  a  practical  test  at  the  Washing- 
ton office  during  the  coming  winter  before  deciding  what  em- 
phasis shall  be  placed  upon  them.  It  should  be  clearly  under- 
stood that  they  are  intended  simply  to  supplement  the  usual 
sea-level  weather  map,  as  auxiliaries  of  any  other  kind  are  em- 
ployed, such  as  the  pressure-change  maps,  and  the  cloud  maps 
now  in  use  in  forecasting.  It  will  be  necessary  only  to  use  a  two- 
syllable  code  word,  as  the  pressure-temperature  word  for  tele- 
graphing the  fractions  of  the  inch  of  pressure  on  the  two  planes, 
since  the  integral  inches  can  readily  be  inferred.  The  study 
of  these  charts  has  developed  many  new  ideas  which  it  would 
be  impossible  to  explain  in  a  short  paper,  and  there  is  no  little 
novelty  of  thought  involved.  It  will  require  practise  to  make 
good  use  of  all  three  charts  simultaneously,  as  they  are  very 
different  from  one  another,  but  as  there  may  be  some  interest 
in  the  matter  among  the  forecast  officials  I  have  added  certain 
precepts  or  brief  statements,  derived  as  the  result  of  my  own 
experience  and  studies. 

1.  Direction  of  the  storm  tracks. — These  follow  closely  the  trend 
of  the  isobars  on  the  10,000-foot  plane,  reference  being  made 
to  the   10,000-foot  isobars  that  are  closely    packed  together 
and  are  lying  well  to  the  south  of  the  center  of  the  cyclones, 
no  regard  being  paid  to  the  northern  curves  which  are  dis- 
torted by  other  influences  and  represent  special  features  of 
the  circulation. 

2.  The  velocity  of  advance. — This  is  very  closely  proportional 
to  the  density  with  which  the  isobars  south  of  the  cyclone  are 
compressed,  a   strong   gradient  indicating   a  quick  advance, 
while  a  wide  gradient  with  straggling  isobars  indicates  that  the 
velocity  of  the  movement  will  be  slow. 

3.  The  areas  of  precipitation. — To  the  eastward  of  the  Rocky 
Mountain  Divide  these  are  approximately  marked  out  by  the 
crossing  of  the  isobars  on  the  3500-foot  plane  at  a  good  angle 
beneath  those  on  the  10,000-foot  plane.     This  is  especially  true 
of  the  months  from  November  to  April,  inclusive.     In  the  sum- 
mer months,  May  to  October,  if  the  two  sets  of  isobars  are 
crowded  together  and  nearly  parallel,  there  is  probability  of 
rainfall  in  the  midst  of  them.     This  rule  seems  to  be  nearly 
true  for  the  north  Pacific  and  north  Plateau\listricts  through- 
out the  year.     The  relative  positions  of  the  low  areas  and  the 
high  areas  is  of  great  significance.     On  the  Pacific  coast  when 


a  high  area  is  to  the  south  and  a  low  area  to  the  north,  these 
crowded  isobars  bring  precipitation  when  they  run  directly 
from  the  ocean  to  the  land.  If  the  high  area  is  well  to  the 
north,  with  the  low  area  far  inland,  and  the  isobars  run  from 
the  northwest  or  north,  the  tendency  to  cause  precipitation  is 
much  diminished.  The  area  of  precipitation  is  on  the  western 
side  of  the  cyclones  of  the  middle  and  north  Plateau  districts, 
but  it  shifts  to  the  eastern  side  as  the  cyclone  passes  over  the 
Rocky  Mountain  slope.  This  makes  difficult  the  forecasting 
for  precipitation  in  the  States  of  the. slope. 

If  the  cyclone  is  on  the  southern  Plateau  or  the  southern 
slope  and  a  high  area  is  to  the  eastward  in  the  Gulf  States, 
the  3500-foot  isobars  usually  open  out  widely  to  the  south 
and  the  region  of  the  underflow  marks  out  the  precipitation 
area  very  definitely.  If  the  cyclone  is  located  far  to  the  north, 
over  the  Missouri  Valley,  the  southern  ends  of  the  3500-foot 
isobars  are  usually  smooth,  unbroken  curves,  and  although 
there  may  be  a  well-marked  underflow  region,  the  precipita- 
tion area  is  to  be  made  much  smaller  than  in  the  preceding 
case  and  placed  well  around  on  the  north  side  of  the  cyclone. 
The  precipitation  area  is  apt  to  be  confined  to  the  closed  iso- 
bars surrounding  the  center.  The  difference  between  these 
cases  lies  in  the  fact  that  the  underflowing  current  in  the 
southern  cyclone  is  full  of  moisture  from  the  Gulf  of  Mexico, 
but  in  the  northern  cyclone  it  is  much  drier,  even  to  the  ex- 
tent of  being  without  precipitation.  The  two  types  here  men- 
tioned will  require  study  and  practise  for  their  differentiation, 
but  a  working  knowledge  of  the  difference  is  easily  acquired. 
When  the  cyclone  is  east  of  the  Mississippi  River,  its  passage 
eastward  or  northeastward  is  closely  controlled  by  the  10,000- 
foot  plane  isobars.  If  the  cyclone  is  on  the  Atlantic  coast,  a 
high-pressure  area  following  it  from  the  southwest  should  be 
interpreted  as  meaning  that  a  rapid  clearing  will  follow  over 
the  region  of  precipitation  in  the  rear  of  the  cyclone.  When 
the  cyclone  is  over  the  Lake  region  and  a  second  depression 
is  over  the  Gulf  of  St.  Lawrence,  if  the  isobars  loop  north- 
ward over  the  Middle  States  between  the  two  lows,  the  area  of 
precipitation  is  quite  general  from  New  England  to  Minnesota. 

4.  Penetration  into  the  higher  levels. — In  the  winter  months, 
December  to  March,  the  heads  of  the  cyclones  do  not  pene- 
trate very  much  above  the  two-mile  level,  but  in  the  summer 
months,  June  to  September,  they  are  apparently  about  four 
miles  high.  In  these  seasons,  respectively,  the  power  of  an 
individual  storm  is  measured  by  its  penetration  into  the  higher 
levels  and  is  proportional  to  it.  In  the  winter  the  upper  strata 
are  cold  and  drift  rapidly  eastward,  and  these  two  causes  de- 
plete the  intruding  cyclonic  head;  in  the  summer  the  cool 
strata  are  much  higher  and  they  move  slowly,  so  that  an  up- 
lifting cyclone  finds  little  to  check  its  development.  This 
principle  is  seen,  also,  in  the  action  of  cumulo-nimbus  clouds 
in  summer.  Allowing  for  relative  differences  of  the  seasons, 
the  action  of  the  upper  strata  upon  cyclones  is  always  essen- 
tially the  same. 

While  there  are  several  such  general  principles  as  these  to 
be  acquired  by  practise,  it  is  yet  true  that  the  distinctive 
weather  types  are  fewer  in  number  and  simpler  in  form  on 
the  3500-foot  and  the  10,000-foot  planes  than  on  the  sea  level, 
and  apparently  their  action  is  much  less  fluctuating  and  de- 
ceptive. This  is  a  decided  advantage  in  studying  the  fore- 
cast problems,  which  now  suffer  by  their  great  complexity  on 
the  sea-level  plane.  In  any  preliminary  study  of  the  new 
charts  there  is  likely  to  be  some  confusion  of  mind,  due  to  the 
novelty  of  the  isobaric  structure  and  the  intrinsic  differences 
of  configuration  between  the  several  planes.  This  mental  state 
will  be  cleared  up  by  practise,  and  it  will  be  found  that  a  real 
addition  has  been  made  in  the  understanding  of  the  prevailing 
storm  action.  Further  advantage  to  be  derived  from  an  intro- 
duction of  the  isotherms  on  the  upper  planes  will  probably 
increase  the  efficiency  of  this  system  in  other  ways. 


xxxii— 67.  Chart  Xn.    Isobars  on  the  sea  level,  the  3500-foot,  and  the  10,000-foot  planes. 


IPS'       ray*        ss°        so"        ss°        so 


— 68.        Chart  XTTT.    Components  of  pressure  on  the  3500-foot  and  the  10, 000- foot  planes. 


Fig,.  66.     Isobars.  (nor/Tra/  6/arc/r, arbnor/na/ red  //rres.) 


66.     Isobars.  (horma/  b/ack,  abfiormar/  red  h'nes.) 


3,300 f 006  ievei. 
Febriia-ry.  3,  79O3 . 


—  69. 


Chart  XT7. — Typical  distribution  of  normal  and  abnormal  isobars. 


XXXII— 70. 

Chart  XV.    Typical  normal  and  abnormal  isotherms  showing  the  positions  of  the  maximum 

excess  and  deficiency  of  heat. 


—  /O 

Fig.  74.     Tern 


3O.30 


30.20 


SO 


30.00       30.  JO 


'iq  73.     Jsobar-s  and  Jsotherm&  ort  the  T^aCher~Jtf/zJpJ:br~lf'ebr~uce-ru  27,19O3 . 


VII.— THE  AVERAGE  MONTHLY  VECTORS  OF  THE  GENERAL  CIRCULATION  IN  THE  UNITED  STATES. 


In  Table  9,  page  144,  Annual  Report  of  the  Chief  of  the 
Weather  Bureau,  1898-1899,  may  be  found  the  data  resulting 
from  the  nephoscope  observations  taken  in  the  international 
cloud  year,  189G-1897,  which  were  made  to  determine  the  gen- 
eral motions  of  the  atmosphere  over  the  United  States.  In 
Table  33,  page  409,  of  the  same  volume,  is  given  a  summary 
of  the  resulting  general  velocities  as  annual  normals.  It  re- 
mains to  compute  the  mean  monthly  normal  vectors  of  the 
circulation,  and  it  has  been  done  by  the  methods  used  in  com- 
puting similar  vectors  for  the  West  Indies,  so  that  but  few 
preliminary  remarks  are  needed  in  this  connection.  The 
method  now  in  use  in  the  Weather  Bureau  of  determining  the 
monthly  direction  of  the  wind  at  a  station  is  really  inadequate 
to  the  requirements  of  modern  science,  which  demands  an  ac- 
curate knowledge  of  the  azimuth  direction  and  velocity  of  the 
wind.  The  method  referred  to  consists  in  counting  the  num- 
ber of  times  the  wind  was  reported  on  each  of  the  eight  car- 
dinal points,  N.,  NE.,  E.,  etc.,  and  assigning  as  the  monthly 
direction  that  which  has  the  plurality  of  numbers.  This  gives 
no  true  resultant  direction  and  takes  no  account  of  the  veloc- 
ity of  the  wind  prevailing  at  each  observation.  A  second 
method  of  reducing  wind  observations,  which  is  somewhat 
more  accurate  than  the  former,  consists  in  assuming  an  equal 
velocity  for  each  wind  and  combining  the  frequency  numbers 
by  using  Lambert's  formula  or  its  equivalent.  This  system 
gives  a  true  resultant  direction  for  winds  of  uniform  velocity, 
but  where  the  winds  are  variable  in  force,  as  well  as  in  direc- 
tion, this  is  also  insufficient.  Many  examples  of  inaccurate 
resultants  can  be  given  when  the  individual  velocities  are  not 
constantly  the  same. 

The  vectors  of  Table  16,  and  figs.  77  to  88,  Charts  XI,  XII, 
and  XIII,  "Average  monthly  vectors  of  the  general  circulation," 
have  been  computed  accurately  by  resolving  each  vector  Vt  <f, 
as  observed,  into  its  north  to  south  and  west  to  east  components, 
taking  the  algebraic  sum  of  each,  and  thence  computing  the 
mean  component  for  the  series,  in  this  case  for  each  month  of 
the  year.  Then  the  resultant  vectors  in  velocity  and  azimuth 
were  constructed,  and  appear  in  Table  16  under  the  columns 
V,  if.  Since  the  resultant  vectors  in  the  lower  cloud  level  and 
at  the  surface  are  very  small,  I  have  also  computed  the  mean 
motion  of  the  wind  for  each  month  without  regard  to  the 
azimuth  direction,  and  this  is  given  under  Vr  In  the  middle 
and  the  upper  cloud  strata  the  azimuth  directions  are  not  so 
variable  as  nearer  the  surface,  and  hence,  there  is  less  differ- 
ence between  the  values  of  V1  and  V.  The  resultant  vectors 


V,  <p  have  been  plotted  in  two  arrangements,  the  first  giving 
the  vectors  of  the  month  for  each  cloud  system  terminating 
on  the  same  vertical  lines,  which  permits  a  ready  inspection  of 
the  relative  motion  in  the  different  levels  for  each  month  of 
the  year.  The  second  arrangement  gives  the  vectors  for  June 
"ending  on  one  vertical  line,  while  those  for  the  other  months 
follow  in  a  broken  line,  which  shows  at  a  glance  the  trend  of 
the  circulation  throughout  the  year  in  the  several  cloud 
groups.  It  has  been  convenient  to  divide  the  clouds  into 
three  groups,  (1)  the  lower  clouds  (stratus,  cumulus,  strato- 
cumulus),  (2)  the  middle  clouds  (alto-stratus,  alto-cumulus), 
and  (3)  the  upper  clouds  (cirro-cumulus,  cirro-stratus,  cirrus), 
which  do  not  differ  greatly  among  themselves  in  velocity. 
The  average  height  of  group  (1),  lower  clouds,  is  2000  meters; 
of  group  (2),  middle  clouds,  5000  meters,  and  of  group  (3), 
upper  clouds,  9000  meters,  as  determined  by  the  theodolite 
observations  at  Washington,  in  1896-1897. 

We  make  the  following  remarks  on  the  vectors  of  Charts  XI 
to  XIII.  The  northern  group  of  stations,  St.  Paul,  Detroit, 
Cleveland,  Buffalo,  Louisville,  Blue  Hill,  Washington,  Waynes- 
ville,  and  Ocean  City,  all  lie  in  the  strong  eastward  drift  to 
the  north  of  the  high  pressure  belt  of  the  general  circulation ; 
Kansas  City,  Abilene,  and  Vicksburg,  lie  in  the  midst  of  this 
belt,  while  Key  West  is  on  the  southern  border  of  it  and  has 
some  of  the  characteristics  of  the  West  Indian  group  of  sta- 
tions. The  northern  stations  in  the  upper  levels  have  strong 
eastward  components,  and  in  the  lower  levels  a  turbulent  cir- 
culation with  small  resultant  vectors.  Louisville  seems  to 
have  something  like  a  personal  equation,  which  has  magnified 
the  vectors  a  little  above  the  apparent  average  that  the  en- 
tire set  would  suggest,  while  Cleveland,  on  the  other  hand, 
seems  to  have  a  diminished  set  of  vectors.  It  is  not  possible 
to  show  from  the  observations  what  change,  if  any,  ought  to 
be  introduced  by  means  of  a  modifying  factor.  Besides  the 
relative  lengths  of  the  vectors  in  the  different  levels  it  is  in- 
teresting to  note  the  north  and  south  components  at  the  sev- 
eral stations.  Thus,  at  St.  Paul  and  also  at  Kansas  City,  there 
is  a  northward  component  in  the  cirrus  levels;  this  component 
prevails  at  all  levels  at  Abilene.  At  Vicksburg  the  vectors  are 
generally  small,  and  they  are  westward  during  certain  months 
in  the  lower  strata.  At  Key  West  the  westward  component  pre- 
vails in  the  lower  levels,  but  the  eastward  in  the  cirrus  level, 
as  in  the  Cuban  stations  generally. 

It  is  desirable  to  extend  such  vector  computations  to  various 
portions  of  the  earth  in  order  to  obtain  the  data  needed  in 
dynamic  meteorology. 

41 


42 

TABLE  16. — Average  monthly  vectors  of  the  general  circulation  in  the  United  States  at  four  levels. 

1.  ST.  PAUL,  MINN. 


1896-97. 

Velocity  in  meters  per  second. 

Wind. 

St.,  Cu.,  S.  Cu. 

A.  S.,  A.  Cu. 

Ci.  Cu.,  Ci.  S.,  Ci. 

v* 

V 

9 

?, 

V 

<P 

v, 

V 

V 

r, 

V 

f 

3.9 
4.1 
4.1 
4.1 
4.0 
3.7 

3.6 
3.6 
3.5 
3.5 
3.6 
3.7 

1.7 
1.5 
1.1 
0.5 
0.0 
0.5 

0.8 
1.0 
1.2 
1.4 
1.5 
1.4 

0 

48 
37 
27 
7 
180 
174 

163 
142 

126 
107 
91 
69 

27.6 

27.4 
26.4 
25.2 
23.6 
22.4 

21.8 
21.4 
22.0 
22.8 
24.0 
25.6 

16.8 
14.4 
12.2 
10.0 
8.2 
7.6 

8.0 
9.0 
11.4 
14.2 
17.2 
18.0 

o 
80 
78 
81 
87 
92 
102 

103 
102 
96 
91 
86 
82 

52.5 
54.5 
54.0 
52.5 
50.0 
48.5 

46.0 
45.0 
45.0 
46.0 
49.0 
50.5 

38.0 
29.5 
20.5 
14.5 
12.0 
12.5 

18.5 
26.0 
35.0 
40.0 
42.0 
41.5 

O 

90 
91 
97 
109 
122 
122 

113 
106 
100 
96 
92 
90 

72.9 
72.9 
72.0 
66.6 
71.1 
55.8 

54.0 
52.2 
53.1 
55.8 
63.0 
70.2 

36.9 
16.2 
10.8 
14.5 
23.4 
39.6 

48.6 
54.9 
58.5 
57.6 
54.0 
46.8 

o 
95 
117 
158 
150 
128 
113 

106 
102 
98 
93 
91 
90 

February                    

March                  

April         

Mav 

June      

July        .  .                 

August            

September  

October    

November  

December             

2.  KANSAS  CITY,  MO. 


January  ~  

4.  1 

1.1 

79 

22.0 

12.0 

74 

27.0 

23.5 

76 

40.5 

36.9 

9 

February   

4.1 

0.9 

86 

21.6 

11.0 

75 

27.5 

23.5 

75 

42.3 

35.1 

9 

March     

3.9 

0.5 

117 

19.8 

9.6 

79 

25.0 

20.5 

77 

36.0 

28.8 

9 

April   

3.6 

0.6 

168 

17.6 

8.0 

83 

20.0 

16.0 

82 

27.0 

24.6 

10 

Mav  . 

3.4 

0.9 

193 

15.6 

6.2 

76 

15.0 

12.0 

92 

18.9 

18.9 

11 

June                    

3.3 

1.1 

207 

14.0 

5.2 

91 

12.0 

9.0 

111 

15.3 

18.0 

13 

Julv  . 

3.  1 

1.2 

211 

14.0 

5.4 

90 

11.0 

7.5 

121 

13.5 

18.0 

13 

August   '  

3.1 

1.1 

212 

14.0 

5.6 

90 

11.0 

6.5 

122 

15.3 

18.0 

14 

September  

3.3 

0.9 

206 

15.0 

6.6 

85 

13.0 

7.5 

97 

18.0 

18.0 

13 

October                                 

3.4 

0.5 

180 

16.0 

8.0 

83 

15.5 

10.0 

82 

24.3 

18.0 

12 

November         

3.6 

0.5 

120 

18.0 

9.8 

80 

20.0 

15.5 

76 

30.6 

22.5 

10 

December      

3.8 

0.9 

85 

20  0 

11.0 

75 

23.5 

20.0 

76 

36.0 

29.7 

0 

3.  ABILENE,  TEX. 


January                  

4.5 

1.2 

128 

14.6 

12.0 

116 

24.5 

23.5 

134 

41.4 

36.0 

125 

February       

4.8 

1.1 

130 

15.2 

5.6 

120 

25.0 

25.0 

132 

44.1 

42.3 

126 

March       

4.8 

1.  1 

164 

14.2 

5.4 

147 

24.0 

22.0 

131 

41.4 

39.6 

125 

April   

4.5 

1.5 

182 

12.6 

5.4 

165 

20.0 

18.0 

128 

34.2 

32.4 

124 

May 

4.3 

2.1 

192 

10.8 

5.2 

180 

15.0 

13.0 

129 

25.2 

20.7 

129 

June                      .  .                    .       

4.0 

2.6 

196 

9.0 

4.8 

193 

11.0 

8.0 

132 

18.0 

9.0 

135 

July              

3.9 

2.7 

197 

8.0 

4.0 

206 

10.0 

3.0 

129 

13.5 

2.7 

180 

August          

3.7 

2.5 

195 

8.0 

3.6 

213 

10.0 

1.5 

135 

10.8 

2.7 

161 

September  

3.7 

2.0 

193 

8.8 

4.0 

203 

11.0 

3.5 

135 

14.4 

3.6 

166 

October 

3.9 

1  5 

173 

10  0 

4.2 

182 

15.0 

8  5 

126 

18.9 

16.2 

124 

November 

4.  1 

1  2 

147 

11  4 

5.2 

159 

18.  5 

15.0 

132 

27.0 

19.8 

118 

December     ...                             ... 

4.4 

1.3 

128 

13.4 

5.8 

137 

22.5 

21.0 

133 

34.2 

28.8 

118 

4.  VICKSBURG,  MISS. 


January  

2  9 

0.5 

270 

8.2 

3.0 

98 

12.0 

13.5 

96 

18.9 

25.2 

94 

February  

3.2 

0.2 

248 

9.0 

4.4 

101 

15.0 

14.0 

98 

25.2 

26.1 

87 

March  

3.5 

0.4 

113 

9.0 

4.8 

112 

15.0 

12.5 

97 

27.0 

25.2 

85 

April   ... 

3.3 

0.9 

90 

8  0 

3  2 

120 

14  0 

11.0 

92 

25.2 

18.0 

90 

May.. 

3.  1 

1  2 

84 

6.8 

2.0 

126 

10.5 

8.5 

90 

20.1 

12.6 

94 

June  

2.8 

1.3 

78 

5.6 

0.4 

90 

8.0 

5.0 

84 

16.2 

7.2 

114 

Julv 

2.6 

1  i 

70 

4  8 

0.4 

0 

6  0 

2  5 

78 

12.6 

3.6 

180 

August  

2  3 

0.8 

63 

4.4 

0  2 

313 

5.0 

1.0 

60 

9.9 

4.5 

206 

September  

2.3 

0.  3 

26 

4.4 

0.4 

245 

5.5 

1.0 

130 

9.0 

1.8 

180 

October  

2.4 

0.4 

276 

4.8 

1.0 

201 

6.5 

3.0 

149 

9.0 

4.5 

90 

November  

2.6 

0.8 

267 

5.6 

2.0 

173 

9.0 

6.0 

121 

10.8 

11.7 

72 

December 

2.7 

0.8 

263 

6.2 

2  2 

146 

11.0 

8.5 

104 

15.3 

16.2 

71 

43 


TABLE  16. — Average  monthly  vectors  of  the  general  circulation,  etc. — Continued. 

5.  LOUISVILLE,  KY. 


1896-97. 

Velocity  in  meters  per  second. 

Wind. 

St.,  Cu.,  St.  Cu. 

A.  S.,  A.  Cu. 

Ci.  Cu.,  C.  S.,  Ci. 

V, 

V 

r 

v, 

V 

9 

v, 

V 

f 

vi 

V 

r 

January           

4.0 
4.1 
4.1 
4.0 
3.7 
3.5 

3.2 
3.0 
2.9 
3.1 
3.3 
3.6 

2.4 
2.2 
1  9 
1.4 
0.9 
0.6 

0.6 
0.6 
0.8 
0.9 
1.7 
2.0 

o 
130 
128 
131 
132 
124 
108 

104 
104 
114 
141 

128 
132 

25.4 
25.2 
24.0 
22.0 
18.0 
15.4 

14  4 
14.4 
15.6 
17.6 
20.4 
23.2 

23.6 
22.6 
20.6 
18.0 
15.0 
12.6 

11.6 
12.0 
13.8 
16.8 
20.4 
22.0 

O 

87 
84 
82 
79 
80 
81 

86 
93 
100 
101 
100 
95 

49.0 
48.5 
42.5 
35.0 
27.0 
24.0 

24.0 
25.5 
30.0 
35.5 
41.5 
46.5 

43.5 

40.5 
33.0 
26.0 
20.5 
18.5 

19.5 
21.5 
26.0 
31.5 
38.0 
43.0 

o 

105 
104 
97 
88 
78 
73 

77 
81 
90 
97 
103 
105 

63.0 
60.3 
52.2 
41.4 
34.2 
28.8 

29.7 
34.2 
39.2 
52.2 
58.5 
61.2 

59.4 
54.0 
45.0 
37.8 
30.6 
28.8 

27.0 
30.6 
36.0 
43.2 
49.5 
55.8 

o 
90 
94 
96 
87 
76 
71 

67 
75 
84 
95 
104 
103 

April                        

June                         .       

July 

August                          

September  

November                               ... 

December           

6.  DETROIT,  MICH. 


January        

5.0 

3.1 

117 

40.6 

33.2 

93 

41.5 

30.5 

100 

55.8 

52.2 

91 

February   

5.1 

2.8 

111 

38.8 

31.2 

92 

42.0 

35.5 

98 

54.0 

52.  2 

91 

March                                          

5.0 

2.4 

105 

35.0 

28.0 

90 

40.0 

33.5 

97 

50  4 

48  6 

88 

April             

4.6 

2.0 

101 

29.2 

23.2 

84 

37.5 

30.0 

94 

45  9 

45.0 

83 

May 

4.  1 

1.5 

98 

23  4 

19.0 

80 

34  0 

26  0 

91 

43  2 

41  4 

74 

June 

3.6 

0.9 

96 

20.2 

16.  2 

75 

31.5 

24  0 

88 

42  3 

40  5 

63 

July 

3.4 

0  8 

103 

19  0 

14  4 

75 

31  5 

22  5 

86 

42  3 

39  6 

61 

3.4 

0.9 

119 

19  6 

13.6 

81 

32  0 

21  0 

87 

43  2 

40  5 

63 

September            ...       

3.6 

1.5 

122 

22.0 

13.8 

90 

34.5 

23  0 

92 

46.8 

40  5 

70 

October  

4.  1 

2.0 

122 

26.8 

15.8 

97 

37.0 

25.0 

95 

54.0 

44.  1 

80 

4.4 

2  6 

121 

34  0 

20  4 

96 

40  0 

29  0 

99 

56  7 

48  9 

88 

December                           

4.8 

3.0 

119 

40.0 

27.6 

95 

42  0 

32  0 

99 

58.5 

49  5 

89 

7.  CLEVELAND,  OHIO. 


January 

5.3 

3  3 

106 

22  6 

17  4 

103 

22  5 

22  5 

119 

41  4 

33  3 

93 

February                 ...             .               

5.4 

3.2 

103 

22.4 

17  0 

104 

23  5 

21.0 

116 

39.6 

34  2 

91 

March     '.  

5.1 

2.8 

99 

21.0 

15.0 

102 

22  5 

17.5 

106 

36.0 

32.4 

90 

April  

4.6 

2.4 

90 

17.6 

12.0 

101 

20.0 

15.0 

98 

27.0 

27.0 

86 

May 

4.  1 

2.0 

79 

14  0 

9  4 

94 

18  5 

13  5 

91 

23.4 

20  7 

82 

June             

3.7 

1.8 

70 

12  2 

8.0 

86 

16.0 

12.5 

85 

18.9 

16.2 

71 

July 

3  6 

1  5 

61 

11  4 

7  8 

72 

15  5 

13.0 

83 

18  0 

14  4 

68 

August     

3.7 

1.4 

60 

12  0 

8  2 

63 

16  0 

14.5 

80 

18.0 

14.4 

68 

September  

4.2 

1.5 

72 

14  0 

9.0 

63 

17.  5 

16.0 

82 

19.8 

17.  1 

75 

October 

4  6 

1  8 

90 

16  4 

>      10  2 

70 

19.5 

18.5 

86 

25  2 

19.8 

76 

November  

5.0 

2.3 

102 

18  4 

12  0 

82 

21.0 

19.5 

90 

32.4 

25.2 

83 

December  

5.2 

2.8 

109 

20.4 

14  4 

93 

23.0 

20.0 

94 

37.8 

30.7 

85 

8.  BUFFALO,  N.  Y. 


January 

5  7 

4  2 

84 

27  4 

17  0 

86 

59  0 

44.5 

89 

51.3 

51  3 

7E 

February    

5  7 

4  1 

87 

26  4 

16  4 

84 

58.5 

43  0 

88 

53.2 

47.7 

75 

March  

5.7 

3  7 

93 

24  0 

15.0 

87 

54.0 

36.0 

88 

36.0 

38.7 

7£ 

April 

5  4 

3  2 

104 

20  6 

12  8 

91 

45  0 

30.5 

89 

33  0 

32  4 

8( 

May  

5  3 

2  9 

112 

16  8 

10  2 

96 

31.5 

23.  5 

92 

33.3 

29.7 

9( 

June  

5  0 

2.6 

121 

14  0 

9.6 

102 

25.0 

18.0 

97 

35.1 

29.7 

M 

July  

4  9 

2.3 

126 

12  0 

9  8 

104 

20  0 

15.5 

105 

36.9 

30  6 

105 

August  

4.7 

2.3 

127 

13.  2 

10.0 

105 

19.5 

16.5 

108 

41.4 

33.3 

104 

September.  .  . 

4  8 

2  3 

126 

17  0 

10  8 

102 

17  0 

19  5 

104 

45.9 

38.7 

10( 

October  

5.0 

2.2 

119 

22  0 

12.2 

96 

27  0 

23  5 

96 

52.2 

45.0 

9E 

November  

5.  1 

2.4 

110 

25.4 

14.4 

91 

36.0 

30.5 

94 

54.0 

51.3 

9( 

December  .... 

5  4 

3  2 

105 

27  2 

16  4 

87 

48.0 

39  0 

91 

55  8 

52  2 

§l 

44 

TABLE  16. — Average  monthly  vectors  of  the  general  circulation,  etc. — Continued. 

9.  BLUE  HILL,  MASS. 


1896-97. 

Velocity  in  meters  per  second. 

Wind. 

St.,  Cu.,  S.  Cu. 

A.  S.,  A.  Cu. 

Ci.  Cu.,  Ci.  S.,  Ci. 

v, 

V 

r 

V, 

V 

9 

Fi 

V 

f 

v, 

F 

9 

January                         "... 

7.6 
7.2 
6.8 
6.4 
6.2 
6.1 

6.2 
6.3 
6.8 
7.0 
7.3 
7.6 

4.6 
4.5 
3.7 
2.6 
2.4 
2.3 

2.3 
2.3 
2.3 
2.5 
2.8 
3.6 

0 

68 
62 
61 
88 
116 
126 

129 
130 
125 
114 
98 
80 

24.2 
23.6 
22.0 
20.4 
19.2 
18.0 

17.6 
17.6 
18.6 
20.2 
22.0 
23.4 

12.4 
12.2 
11.4 
10.6 
9.6 
8.4 

8.4 
9.4 
10.2 
10.0 
9.4 
10.8 

o 
73 
75 
76 
80 
84 
89 

101 
117 
124 
120 
90 
74 

38.5 
35.5 
32.0 
28.0 
24.0 
22.0 

19.0 
20.0 
25.0 
31.0 
36.0 
38.5 

32.0 
30.5 
26.5 
22.0 
19.0 
17.5 

16.5 
18.5 
22.0 
27.0 
32.0 
32.5 

O 

97 
92 
89 
87 
85 
88 

93 
103 
109 
113 
111 
106 

54.0 
49.5 
41.4 
35.1 
28.8 
27.0 

27.0 
27.9 
31.5 
38.7 
45.0 
52.2 

46.8 
45.0 
38.7 
32.4 
26.  1 
23.4 

22.5 
22.5 
27.0 
33.0 
40.5 
46.8 

0 

87 
83 
80 
83 
87 
91 

98 
99 
101 
99 
96 
93 

February              

March   

April   

May 

June                                               .  . 

July                      

August     

September  

November                           

December                        

10.  WASHINGTON,  D.  C. 


January  

4.1 

2.0 

34 

14.0 

8.6 

101 

27.5 

25.0 

90 

47.7 

45.9 

91 

February                                           

3.9 

1.7 

23 

14.0 

8.4 

106 

28.  5 

24.0 

97 

50.4 

45  9 

92 

March                       .                  

3.6 

1.4 

39 

13.4 

8.0 

108 

26.5 

22.5 

101 

45  0 

43.2 

92 

April                                

3.2 

1.0 

49 

12.0 

7.4 

111 

22.5 

19.5 

104 

36.0 

35  1 

91 

May               .           

2.8 

0.6 

73 

11.0 

6.0 

111 

18.5 

16.0 

107 

27.0 

26.  1 

90 

June       .  .           

2.5 

0.5 

110 

10.0 

5.2 

104 

15.0 

12.0 

100 

23.4 

19.8 

90 

July    . 

2.3 

0.5 

117 

8.8 

4.6 

95 

13.5 

10.5 

95 

19.8 

17.1 

90 

2.3 

0.5 

117 

8.2 

4.8 

81 

13.5 

10.0 

90 

19.8 

18  0 

88 

September              .      .                

2.5 

0.5 

90 

8.8 

5.8 

72 

15.0 

11.5 

85 

21.6 

20.7 

87 

October              

2.9 

0.7 

65 

10.2 

7.4 

73 

18.0 

15.0 

81 

27.0 

24.3 

87 

November                '  

3.2 

1.2 

50 

12.2 

8.4 

76 

21.0 

14.5 

79 

31.5 

31.5 

90 

December  

3.6 

1.7 

40 

14.0 

8.0 

85 

25.0 

17.5 

82 

37.8 

38.7 

90 

11.  WAYNESVILLE,  N.  C.        12.  OCEAN  CITY,  MD. 


2.9 

1.6 

62 

15.8 

11.6 

91 

36.0 

35.0 

108 

53.  1 

51.3 

94 

February                       

2.7 

1.4 

59 

15.2 

11.2 

92 

35.5 

35.0 

107 

54.0 

51.3 

94 

March                 

2.3 

0.9 

57 

13.2 

10.0 

90 

34.0 

31.5 

109 

45.0 

45.0 

92 

April                   

1.9 

0.5 

56 

12.6 

8.0 

88 

30.0 

26.5 

108 

36.0 

35.1 

91 

May 

1.6 

0.1 

107 

8.4 

6.0 

80 

25.0 

19.0 

103 

27.0 

25.2 

91 

1.4 

0.3 

180 

6.8 

4.8 

70 

18.5 

15.0 

95 

18.0 

14.4 

90 

July                                          

1.3 

0.5 

180 

6.0 

4.6 

63 

13.0 

10.0 

91 

10.8 

9.0 

84 

August                   .                 

1.3 

0.4 

167 

6.0 

4.8 

68 

11.0 

10.5 

90 

9.0 

9.0 

84 

September     

1.4 

0.4 

120 

8.0 

6.4 

67 

14.0 

14.0 

94 

11.7 

14.4 

86 

October  

2.0 

0.6 

78 

10.4 

8.0 

85 

20.0 

20.5 

98 

18.9 

26.  1 

88 

November 

2.6 

1.  1 

68 

13.6 

9.8 

87 

26.5 

27.5 

102 

28.8 

36.0 

90 

December                    .  .           ... 

2.9 

1.5 

63 

15.6 

11.2 

91 

34.0 

32.0 

105 

39.6 

45.0 

92 

13.  KEY  WEST,  FLA. 


January  

4.6 

2.3 

318 

14.4 

2.4 

215 

20.0 

8.0 

97 

28.8 

26.1 

90 

February                                      .         ... 

4.5 

1.8 

294 

15.2 

4.6 

193 

20.0 

9.5 

106 

27.9 

24.3 

91 

March             ....            

4.3 

1.9 

265 

14.8 

6.4 

197 

17.0 

7.5 

106 

25.2 

19.8 

86 

April       

4.1 

2.4 

251 

13.6 

8.0 

210 

13.5 

4.0 

104 

18.0 

14.4 

69 

May  .  . 

4.2 

2.7 

249 

12.0 

9.0 

221 

10.0 

0.5 

135 

11.7 

10.8 

49 

June  

4.  1 

2.9 

248 

10.4 

8.8 

228 

8.5 

2.0 

270 

17.1 

7.2 

7 

July        

4.0 

2.9 

253 

9.4 

11.0 

244 

7.5 

5.0 

259 

15.3 

5.4 

321 

August  

3.8 

2.9 

261 

8.4 

10.0 

254 

7.5 

5.5 

255 

15.3 

4.5 

308 

September 

3  8 

2  8 

274 

8.4 

8.6 

262 

8.5 

7.0 

249 

9.0 

1.8 

227 

October                        .  .     .  .       .    .       .... 

4.1 

2.7 

289 

9.2 

4.8 

267 

10.5 

5.5 

246 

12.6 

7.2 

120 

November     

4.5 

2.7 

306 

10.2 

2.4 

260 

14.5 

4.0 

235 

18.0 

15.3 

107 

December  

4.6 

2.7 

318 

12.2 

1.8 

229 

17.0 

3.0 

211 

23.4 

19.8 

100 

XXXII— 81. 


Chart  XI.    Average  monthly  vectors  of  the  general  circulation. 


Paul, Minn. 


Fi  r~-5 1  \A  7-7-ariffeme 


i 'r-&tJ4rr-<z  rive  brent . 


jSecorta?  _^  rranqern 


Abilene,  Teoca*. 


XXXII— 82. 


-Chart  XII.    Average  monthly  vectors  of  the  general  circulation. 


Detroit,  Afich. 


c£  ^i  f  r-a.  rty  em  <sn  £ 


XXXII— 83. 


Chart  XIII.    Average  monthly  vectors  of  the  general  circulation. 


Ft.  85,        Blue  Hill,  Mass. 


l  7? 


.  S,  A.  Ca 


Cu,  S,. 


Wfnd 


</    A      «?     O     /V     D 


Z'f  D.C. 


^  77- 


</ 


6"     O     A'     O 


FiriStsldrrarzcfem&rt.  t 


^C/:<s,C/.Cc/,. 


Second  -Arrartgement. 


iSccond^A  r-rartgemen  t 


D 


,  .4.  a/,. 


Fig.  (97. 


<J      F    AS  A    M   t/     c/    A     ,5"     O    A1     D 


Cu,  <5,  . 


-7  "tr-alnjerte. 


-•* 


V. 


W/nc/ 


«/  A  r-rarryern  en  t 


<Sca/e  of  Ms/act  fy 


RETURN     CIRCULATION  DEPARTMENT 

TO—  ^      202  Main  Library 

23110 

LOAN  PERIOD  1 
HOME  USE 

2 

3 

4 

5 

6 

ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS 

Renewals  and  Recharges  may  be  made  4  days  prior  to  the  due  date. 

Books  may  be  Renewed  by  calling     642-3405. 


LIB>-..x.<Y'uj|83I| 

^STAMPED  BELOW 

AUG  i8  198! 

I 

C/HCULAflON  Ui 

sd 

RECEIVE! 

AUG  t  A  ,, 

CIRCULATION 

DEPT 

FORM  NO.  DD6 


UNIVERSITY  OF  CALIFORNIA,  BERKELEY 
BERKELEY,  CA  94720 


[30m-6,'U] 


u.c. 


